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data-dom-id="Pill-react-component-8ce46442-4acd-465f-b801-482ef318c236"></div> <div id="Pill-react-component-8ce46442-4acd-465f-b801-482ef318c236"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Marius Junge</h3></div><div class="js-work-strip profile--work_container" data-work-id="122354538"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates"><img alt="Research paper thumbnail of Complete order and relative entropy decay rates" class="work-thumbnail" src="https://attachments.academia-assets.com/117036703/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates">Complete order and relative entropy decay rates</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Sep 22, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for matrix-valued functions. For quantum Markov semigroups, we obtain that the complete modified logarithmic Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension constant. This estimate is asymptotically tight for a quantum birth-death process. Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6c59821c686a55f86ef98054975c1001" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036703,"asset_id":122354538,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354538"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354538"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354538; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354538]").text(description); $(".js-view-count[data-work-id=122354538]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354538; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354538']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354538, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6c59821c686a55f86ef98054975c1001" } } $('.js-work-strip[data-work-id=122354538]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354538,"title":"Complete order and relative entropy decay rates","translated_title":"","metadata":{"publisher":"Cornell University","grobid_abstract":"We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. 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Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.","publication_date":{"day":22,"month":9,"year":2022,"errors":{}},"publication_name":"arXiv (Cornell University)","grobid_abstract_attachment_id":117036703},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates","translated_internal_url":"","created_at":"2024-07-25T22:49:34.902-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036703,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036703/thumbnails/1.jpg","file_name":"2209.pdf","download_url":"https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Complete_order_and_relative_entropy_deca.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036703/2209-libre.pdf?1721973196=\u0026response-content-disposition=attachment%3B+filename%3DComplete_order_and_relative_entropy_deca.pdf\u0026Expires=1733905077\u0026Signature=Aqcm5kGtNFhyK0MkK9xiY2rMnnMfUSEGUN9gdH4kmbRdIG-qAJcqgHVeiGpPtUrCUTeSj-bYh10RyUKk6cwYA0Pq0nzfHM2dDFHcuRMkashe1UOBfzRnzLsCAbua4Wh5bPXo1R1eBb5L16oIvII7lQCu2nia6oNSHH5sre29lu7OlIm8hxYlN7JrXPof4C-RVYajubj~9pilseo2Y3aa-vfktpPvdd6EuL08OSc5eNuhe6CSW5kH6j3tDFX5j4NsDlYnCFU3veZ7EB3D-W9aiDnoyEUh797KIw~yIxZv8N1h7cdxNVSdLaZzfj8DybgLizrlA-vrc~diK3bbRfKJyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Complete_order_and_relative_entropy_decay_rates","translated_slug":"","page_count":58,"language":"en","content_type":"Work","summary":"We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for matrix-valued functions. For quantum Markov semigroups, we obtain that the complete modified logarithmic Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension constant. This estimate is asymptotically tight for a quantum birth-death process. Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117036703,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036703/thumbnails/1.jpg","file_name":"2209.pdf","download_url":"https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Complete_order_and_relative_entropy_deca.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036703/2209-libre.pdf?1721973196=\u0026response-content-disposition=attachment%3B+filename%3DComplete_order_and_relative_entropy_deca.pdf\u0026Expires=1733905077\u0026Signature=Aqcm5kGtNFhyK0MkK9xiY2rMnnMfUSEGUN9gdH4kmbRdIG-qAJcqgHVeiGpPtUrCUTeSj-bYh10RyUKk6cwYA0Pq0nzfHM2dDFHcuRMkashe1UOBfzRnzLsCAbua4Wh5bPXo1R1eBb5L16oIvII7lQCu2nia6oNSHH5sre29lu7OlIm8hxYlN7JrXPof4C-RVYajubj~9pilseo2Y3aa-vfktpPvdd6EuL08OSc5eNuhe6CSW5kH6j3tDFX5j4NsDlYnCFU3veZ7EB3D-W9aiDnoyEUh797KIw~yIxZv8N1h7cdxNVSdLaZzfj8DybgLizrlA-vrc~diK3bbRfKJyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":43689367,"url":"http://arxiv.org/pdf/2209.11684"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122354532"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354532/q_Chaos"><img alt="Research paper thumbnail of 𝑞-Chaos" class="work-thumbnail" src="https://attachments.academia-assets.com/117036704/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354532/q_Chaos">𝑞-Chaos</a></div><div class="wp-workCard_item"><span>Transactions of the American Mathematical Society</span><span>, May 18, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 < q < 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b3cab1d49d142b1ff2d6de13493bbd61" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036704,"asset_id":122354532,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036704/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354532"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354532"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354532; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354532]").text(description); $(".js-view-count[data-work-id=122354532]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354532; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354532']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354532, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b3cab1d49d142b1ff2d6de13493bbd61" } } $('.js-work-strip[data-work-id=122354532]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354532,"title":"𝑞-Chaos","translated_title":"","metadata":{"publisher":"American Mathematical Society","grobid_abstract":"We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 \u003c q \u003c 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.","publication_date":{"day":18,"month":5,"year":2011,"errors":{}},"publication_name":"Transactions of the American Mathematical Society","grobid_abstract_attachment_id":117036704},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354532/q_Chaos","translated_internal_url":"","created_at":"2024-07-25T22:49:34.019-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036704,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036704/thumbnails/1.jpg","file_name":"S0002-9947-2011-05165-2.pdf","download_url":"https://www.academia.edu/attachments/117036704/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036704/S0002-9947-2011-05165-2-libre.pdf?1721973185=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905077\u0026Signature=DosZsLkWcq8S6HFpv6PXQTWfeJ2OX8TzsX6cuZX9S5JvZBksYjPdEYE6W3DsfF0oeLQmi-vMJ0jaq9bqlX1KjQCnU6gU8SjH~whOQZ66ljTE1tOg2UE8A8ZzcSW3MVXBP5Rj~xsKX~bqP1ee7VXiIoqKv3ia8m5f8ORilYEg2h0QF~IAjlAIHE9fak8UoXFLI4KQbG~Gk1ZUNeXswWS~kfcYun-hVjvi1ZfoQZY2JfatsyZlnlSkmuEM7vw1LoAqGLUbuGAAAMr6yj8uWDtrssMzIQWBvuDdNQMt0ReJsAyLuL86~4NsfjINfXPhpIBdNiR~DSp-5f8Fy7gQguuADg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"q_Chaos","translated_slug":"","page_count":27,"language":"en","content_type":"Work","summary":"We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 \u003c q \u003c 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius 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/></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354528/Relative_Embeddability_of_von_Neumann_Algebras_and_Amalgamated_Free_Products">Relative Embeddability of von Neumann Algebras and Amalgamated Free Products</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Dec 14, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ⊆ M , we have the reduced amalgamated free product * N M is embeddable into (R⊗N 1) ω for some other finite von Neumann algebra N 1 , where R is the hyperfinite II 1 factor.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="957c3cb7dc71ca94803fe53f9ad07c67" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036699,"asset_id":122354528,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036699/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" 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this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ⊆ M , we have the reduced amalgamated free product * N M is embeddable into (R⊗N 1) ω for some other finite von Neumann algebra N 1 , where R is the hyperfinite II 1 factor.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius 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thumbnail of Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery" class="work-thumbnail" src="https://attachments.academia-assets.com/117036728/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354525/Entropy_Estimates_on_Tensor_Products_of_Banach_Spaces_and_Applications_to_Low_Rank_Recovery">Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery</a></div><div class="wp-workCard_item"><span>2019 13th International conference on Sampling Theory and Applications (SampTA)</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Low-rank matrix models have been universally useful for numerous applications starting from class...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. The Schatten-1 norm, also known as the nuclear norm, has been used as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the Schatten-1 norm for low-rankness has a nice analogy with the 1 norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the Schatten-1 norm. Inspired by a recent work on the max-norm-based matrix completion, we provide a unified view on a class of tensor product norms and their interlacing relations on low-rank operators. Furthermore we derive entropy estimates between the injective and projective tensor products of a family of Banach space pairs and demonstrate their applications to matrix completion and decentralized subspace sketching.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="170ed7c832c50b2a5736a519e113f148" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036728,"asset_id":122354525,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036728/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354525"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354525"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354525; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354525]").text(description); $(".js-view-count[data-work-id=122354525]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354525; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354525']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354525, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "170ed7c832c50b2a5736a519e113f148" } } $('.js-work-strip[data-work-id=122354525]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354525,"title":"Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery","translated_title":"","metadata":{"publisher":"IEEE","grobid_abstract":"Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. 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Furthermore we derive entropy estimates between the injective and projective tensor products of a family of Banach space pairs and demonstrate their applications to matrix completion and decentralized subspace sketching.","publication_date":{"day":null,"month":null,"year":2019,"errors":{}},"publication_name":"2019 13th International conference on Sampling Theory and Applications (SampTA)","grobid_abstract_attachment_id":117036728},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354525/Entropy_Estimates_on_Tensor_Products_of_Banach_Spaces_and_Applications_to_Low_Rank_Recovery","translated_internal_url":"","created_at":"2024-07-25T22:49:32.911-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036728,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036728/thumbnails/1.jpg","file_name":"document.pdf","download_url":"https://www.academia.edu/attachments/117036728/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropy_Estimates_on_Tensor_Products_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036728/document-libre.pdf?1721973172=\u0026response-content-disposition=attachment%3B+filename%3DEntropy_Estimates_on_Tensor_Products_of.pdf\u0026Expires=1733905077\u0026Signature=B5zTJE88YDKYzU463g~u9JBlG~Ewlg2p28O72AEIRal16e7r6jJrOOv7KC0WyOlko6S1MBqTKZ1haloPtdu9-PvyPjUiJowLmyU5PHa9z0n3EI5wH6kV72giqhjz6POEiiw9bR6hu5TMhf9sw4cNCN75nWKMOKPy4nBjWhEG~v1PmE~80-3rGO6cNu7xZaPFFYnhYZ2ohJRGgx2VjIKRVbbWwZPSN--e1hcg2mHtT1libjv-sRP~QL-dUSlkA3aqRb~p0xO7brdUB0iBxqG0Fxi86wFipCzOn41ibAQ87jfCs1bsfx1lBO5eowK22XaOXDmy9WbaTUSXHtkUfAoZBA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Entropy_Estimates_on_Tensor_Products_of_Banach_Spaces_and_Applications_to_Low_Rank_Recovery","translated_slug":"","page_count":4,"language":"en","content_type":"Work","summary":"Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. The Schatten-1 norm, also known as the nuclear norm, has been used as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the Schatten-1 norm for low-rankness has a nice analogy with the 1 norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the Schatten-1 norm. Inspired by a recent work on the max-norm-based matrix completion, we provide a unified view on a class of tensor product norms and their interlacing relations on low-rank operators. Furthermore we derive entropy estimates between the injective and projective tensor products of a family of Banach space pairs and demonstrate their applications to matrix completion and decentralized subspace sketching.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117036728,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036728/thumbnails/1.jpg","file_name":"document.pdf","download_url":"https://www.academia.edu/attachments/117036728/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Entropy_Estimates_on_Tensor_Products_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036728/document-libre.pdf?1721973172=\u0026response-content-disposition=attachment%3B+filename%3DEntropy_Estimates_on_Tensor_Products_of.pdf\u0026Expires=1733905077\u0026Signature=B5zTJE88YDKYzU463g~u9JBlG~Ewlg2p28O72AEIRal16e7r6jJrOOv7KC0WyOlko6S1MBqTKZ1haloPtdu9-PvyPjUiJowLmyU5PHa9z0n3EI5wH6kV72giqhjz6POEiiw9bR6hu5TMhf9sw4cNCN75nWKMOKPy4nBjWhEG~v1PmE~80-3rGO6cNu7xZaPFFYnhYZ2ohJRGgx2VjIKRVbbWwZPSN--e1hcg2mHtT1libjv-sRP~QL-dUSlkA3aqRb~p0xO7brdUB0iBxqG0Fxi86wFipCzOn41ibAQ87jfCs1bsfx1lBO5eowK22XaOXDmy9WbaTUSXHtkUfAoZBA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":95988,"name":"Matrix Completion","url":"https://www.academia.edu/Documents/in/Matrix_Completion"},{"id":2720299,"name":"Matrix norm","url":"https://www.academia.edu/Documents/in/Matrix_norm"}],"urls":[{"id":43689355,"url":"http://xplorestaging.ieee.org/ielx7/9006976/9030804/09030989.pdf?arnumber=9030989"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122354520"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354520/Decentralized_sketching_of_low_rank_matrices"><img alt="Research paper thumbnail of Decentralized sketching of low rank matrices" class="work-thumbnail" src="https://attachments.academia-assets.com/117036693/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354520/Decentralized_sketching_of_low_rank_matrices">Decentralized sketching of low rank matrices</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L &lt;&lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\log^6(d_1 + d_2)/\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1b0f1fe5c42b7ab10612dcbcacdbb934" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036693,"asset_id":122354520,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354520"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354520"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354520; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354520]").text(description); $(".js-view-count[data-work-id=122354520]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354520; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354520']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354520, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1b0f1fe5c42b7ab10612dcbcacdbb934" } } $('.js-work-strip[data-work-id=122354520]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354520,"title":"Decentralized sketching of low rank matrices","translated_title":"","metadata":{"abstract":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","publisher":"NeurIPS","publication_date":{"day":null,"month":null,"year":2019,"errors":{}}},"translated_abstract":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","internal_url":"https://www.academia.edu/122354520/Decentralized_sketching_of_low_rank_matrices","translated_internal_url":"","created_at":"2024-07-25T22:49:32.304-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036693,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036693/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036693/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973178=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=YtbDygibkXF8d2TIEzHwYhtxhG8c-4B2bOdchva4ItFSEZa-jI~Bwwmj1kQ0NPmDAUTc4IDM77YoNRqxNilihx2HMSJFAMsKNvhMjMMz96eXlZL3u66E2rRwLIeg5z9YirZi5v9rFPzriSb75zPylledKv2bhEDiF164A~bVFstqidW7AJI5~pnFtaSz8Rc-~L1lK9IgOTxzoin4tSrWPutolrJGWDzX-tOtoSYErujlQC3YcR1wfVB4izWjaWtTB97gWtcDVnZ0OpiOPdL1B4oJmlNApjrJEWgdqG~Y0Y8SWpwtnmeaIXnWuH2FQORggtSodp1QUJcvlKOW-8Rjbg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Decentralized_sketching_of_low_rank_matrices","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117036693,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036693/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036693/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973178=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=YtbDygibkXF8d2TIEzHwYhtxhG8c-4B2bOdchva4ItFSEZa-jI~Bwwmj1kQ0NPmDAUTc4IDM77YoNRqxNilihx2HMSJFAMsKNvhMjMMz96eXlZL3u66E2rRwLIeg5z9YirZi5v9rFPzriSb75zPylledKv2bhEDiF164A~bVFstqidW7AJI5~pnFtaSz8Rc-~L1lK9IgOTxzoin4tSrWPutolrJGWDzX-tOtoSYErujlQC3YcR1wfVB4izWjaWtTB97gWtcDVnZ0OpiOPdL1B4oJmlNApjrJEWgdqG~Y0Y8SWpwtnmeaIXnWuH2FQORggtSodp1QUJcvlKOW-8Rjbg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":117036692,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036692/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036692/download_file","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036692/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973184=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=fT8KhChf36HGXoFChcrpscXPN28s79xjtteQPQReNHbFKEos-y4I2XIUFPOuVsVYFN05JqXgMWZxq9UDRE7UHDipuiv0qQ2gIajTtk1kSSBmP~dVpKifcc-wVB8BYIG7GCNWh2wd2wHieaK4zUynB08iOMFXJBgeW~vQQBEtH~LuPvccK2KbK12eAuZgcYJdQYIWZ3WrCZ48QR6mOjYdGuVVFjSJMN0ItzyRJiZ1XKYTFtS3lv0ANh-jVGL~40hEncHUACXltxB9VE-~tlwFLcHqAE1sNtLD9K~NSEFmQqx0meYmDSkPPNG5mnu4DQYiUmJ8AHDZYTF0u8GIGzlP2w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":95988,"name":"Matrix Completion","url":"https://www.academia.edu/Documents/in/Matrix_Completion"},{"id":322514,"name":"Low-Rank Approximation","url":"https://www.academia.edu/Documents/in/Low-Rank_Approximation"},{"id":2720299,"name":"Matrix norm","url":"https://www.academia.edu/Documents/in/Matrix_norm"}],"urls":[{"id":43689352,"url":"http://papers.nips.cc/paper/9200-decentralized-sketching-of-low-rank-matrices.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122354517"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354517/Capacity_Estimates_for_TRO_Channels"><img alt="Research paper thumbnail of Capacity Estimates for TRO Channels" class="work-thumbnail" src="https://attachments.academia-assets.com/117036687/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354517/Capacity_Estimates_for_TRO_Channels">Capacity Estimates for TRO Channels</a></div><div class="wp-workCard_item"><span>arXiv: Quantum Physics</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Using the notion of TRO&#39;s (ternary ring of operators) and independence from operator algebra ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Using the notion of TRO&#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. This class goes beyond degradable channels. The estimate are based on a &quot;local comparison theorem&quot; for sandwiched R\&#39;enyi relative entropy and complex interpolation. As an application, we discover new small dimensional examples which admit an easy formula for quantum and private capacities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="201c046d008ba2f272ae359a893531c6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036687,"asset_id":122354517,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036687/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354517"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354517"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354517; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354517]").text(description); $(".js-view-count[data-work-id=122354517]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354517; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354517']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354517, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "201c046d008ba2f272ae359a893531c6" } } $('.js-work-strip[data-work-id=122354517]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354517,"title":"Capacity Estimates for TRO Channels","translated_title":"","metadata":{"abstract":"Using the notion of TRO\u0026#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. This class goes beyond degradable channels. The estimate are based on a \u0026quot;local comparison theorem\u0026quot; for sandwiched R\\\u0026#39;enyi relative entropy and complex interpolation. As an application, we discover new small dimensional examples which admit an easy formula for quantum and private capacities.","publication_date":{"day":null,"month":null,"year":2016,"errors":{}},"publication_name":"arXiv: Quantum Physics"},"translated_abstract":"Using the notion of TRO\u0026#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. This class goes beyond degradable channels. The estimate are based on a \u0026quot;local comparison theorem\u0026quot; for sandwiched R\\\u0026#39;enyi relative entropy and complex interpolation. 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Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase 'universal collective rotation channels' for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7e508a7694c6f6360c40eaefd01d1376" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034522,"asset_id":122351833,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351833"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351833"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351833; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351833]").text(description); $(".js-view-count[data-work-id=122351833]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351833; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351833']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351833, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7e508a7694c6f6360c40eaefd01d1376" } } $('.js-work-strip[data-work-id=122351833]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351833,"title":"Quantum error correction and Young tableaux","translated_title":"","metadata":{"grobid_abstract":"A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. 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We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.","grobid_abstract_attachment_id":117034522},"translated_abstract":null,"internal_url":"https://www.academia.edu/122351833/Quantum_error_correction_and_Young_tableaux","translated_internal_url":"","created_at":"2024-07-25T19:01:19.892-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117034522,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034522/thumbnails/1.jpg","file_name":"0405032v2.pdf","download_url":"https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantum_error_correction_and_Young_table.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034522/0405032v2-libre.pdf?1721959986=\u0026response-content-disposition=attachment%3B+filename%3DQuantum_error_correction_and_Young_table.pdf\u0026Expires=1733905077\u0026Signature=CAiz7HcfywV6Bj8bSd1xn5HZPSMRqcJZgTh4oxJUdVlVCCBS~E57PMzCaz2W~5GmeH-3AsbWT5tVTxq5qaQByuhG6Es9TstKAU~EzBy8WyMd25zIdzeT1mOStGPjD~l1NkorZB7PGx-ed9TsEALi5MOqfhMmTQJCfMh2EAFze37h~knr8hqLnH1zMyTkOKNoS8fTm-sujc4v6uc0H452q7UunTNMjVPVNHqdKpW~ONRv0mOKNmBFESOLJyiqcmjfn6JFElzYKHfEixA4OX9JVPNjQbzltOffPaUY0Oyavnr4bdFBGs3-djhkXRVQiY8bQUPLmg~glk7CYZu-wpV-fA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Quantum_error_correction_and_Young_tableaux","translated_slug":"","page_count":25,"language":"en","content_type":"Work","summary":"A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase 'universal collective rotation channels' for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117034522,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034522/thumbnails/1.jpg","file_name":"0405032v2.pdf","download_url":"https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantum_error_correction_and_Young_table.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034522/0405032v2-libre.pdf?1721959986=\u0026response-content-disposition=attachment%3B+filename%3DQuantum_error_correction_and_Young_table.pdf\u0026Expires=1733905077\u0026Signature=CAiz7HcfywV6Bj8bSd1xn5HZPSMRqcJZgTh4oxJUdVlVCCBS~E57PMzCaz2W~5GmeH-3AsbWT5tVTxq5qaQByuhG6Es9TstKAU~EzBy8WyMd25zIdzeT1mOStGPjD~l1NkorZB7PGx-ed9TsEALi5MOqfhMmTQJCfMh2EAFze37h~knr8hqLnH1zMyTkOKNoS8fTm-sujc4v6uc0H452q7UunTNMjVPVNHqdKpW~ONRv0mOKNmBFESOLJyiqcmjfn6JFElzYKHfEixA4OX9JVPNjQbzltOffPaUY0Oyavnr4bdFBGs3-djhkXRVQiY8bQUPLmg~glk7CYZu-wpV-fA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122351832"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122351832/Operator_structures_in_quantum_information_theory"><img alt="Research paper thumbnail of Operator structures in quantum information theory" class="work-thumbnail" src="https://attachments.academia-assets.com/117034506/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122351832/Operator_structures_in_quantum_information_theory">Operator structures in quantum information theory</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Physicists have long recognized that the appropriate framework for quantum theory is that of a Hi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B (H). This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗-algebras and W∗-algebras (with the latter also known as von Neumann algebras). In the 1970&#x27;s these were used extensively in the study of quantum statistical mechanics and quantum field theory. Although at the most basic level, quantum ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="95e909ca033ab8f0b68a8e17cb71f52c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034506,"asset_id":122351832,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034506/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351832"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351832"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351832; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351832]").text(description); $(".js-view-count[data-work-id=122351832]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351832; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351832']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351832, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "95e909ca033ab8f0b68a8e17cb71f52c" } } $('.js-work-strip[data-work-id=122351832]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351832,"title":"Operator structures in quantum information theory","translated_title":"","metadata":{"abstract":"Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B (H). 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Our method is based on the bimodule structure of the derivation space and the technique developed in [18]. Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1a8178eb4dac98cc5920dbbb5b6f02bd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034502,"asset_id":122351823,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351823"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351823"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351823; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351823]").text(description); $(".js-view-count[data-work-id=122351823]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351823; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351823']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351823, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1a8178eb4dac98cc5920dbbb5b6f02bd" } } $('.js-work-strip[data-work-id=122351823]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351823,"title":"Stability property for the quantum jump operators of an open system","translated_title":"","metadata":{"publisher":"Cornell University","grobid_abstract":"We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. 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Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.","publication_date":{"day":14,"month":11,"year":2022,"errors":{}},"publication_name":"arXiv (Cornell University)","grobid_abstract_attachment_id":117034502},"translated_abstract":null,"internal_url":"https://www.academia.edu/122351823/Stability_property_for_the_quantum_jump_operators_of_an_open_system","translated_internal_url":"","created_at":"2024-07-25T19:01:08.330-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117034502,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034502/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034502/2211-libre.pdf?1721960002=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905077\u0026Signature=PlP1vZgB6cHH8w3QpDWwB5nmOaoZuT4KeTl5hdsxW4rhJ3CaTbX1CgpWyU~ImOceLiUNOU1OqjqMmWmUEZ6oPVNKih34KI3s5sIfVg3bRtRNWFd5OBPWlIgNCvoT13VISN1hWHYDTlNdfnljHQXoWR5Yf~~WfeMEqwdBFIstlT6qcAhN-R6-Q9GYx58A17kIvvvvWisawVxoBvIl1yVb9FXUxHnAW7KESu0L-kCTuezJ4YBXy1CNArSD86e7XRkwDdQ1w3OwwR3d0xOLm75BEmsWJMaHK~lqZfsN0pulxHsAfwWe3waahzntWTLO~mkzJ3LCeZp3BhXwO5CI6bRH8g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Stability_property_for_the_quantum_jump_operators_of_an_open_system","translated_slug":"","page_count":25,"language":"en","content_type":"Work","summary":"We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space and the technique developed in [18]. Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117034502,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034502/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034502/2211-libre.pdf?1721960002=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905077\u0026Signature=PlP1vZgB6cHH8w3QpDWwB5nmOaoZuT4KeTl5hdsxW4rhJ3CaTbX1CgpWyU~ImOceLiUNOU1OqjqMmWmUEZ6oPVNKih34KI3s5sIfVg3bRtRNWFd5OBPWlIgNCvoT13VISN1hWHYDTlNdfnljHQXoWR5Yf~~WfeMEqwdBFIstlT6qcAhN-R6-Q9GYx58A17kIvvvvWisawVxoBvIl1yVb9FXUxHnAW7KESu0L-kCTuezJ4YBXy1CNArSD86e7XRkwDdQ1w3OwwR3d0xOLm75BEmsWJMaHK~lqZfsN0pulxHsAfwWe3waahzntWTLO~mkzJ3LCeZp3BhXwO5CI6bRH8g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":117034501,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034501/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034501/download_file","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034501/2211-libre.pdf?1721959997=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905078\u0026Signature=NgopP1jRsfVGjph1ETZM8W2Rrky0YUgBA289aC0u9X6hNiCbixlW9HYr5Q-CI1xLgdNI11ALZaLYNmVwi7FCXxgfoFU0G2ImPUsmJwe4ZYcgKTU9e9ZvMR5xcZ4DJ7BBy-uKq2h~gjjhUNkRly75y1tJ8MdcERUo7MPMlKsEcvxDgygMm3hTvMzKa8W4IRC0kEOf9~XJpsvxO2D1rC0Bc4lf24WiEhvzSn3zui3~2p3hF1-e65id49T1BRFMp5BVhlR9L9iQdyg5xMuMoXl8QItds-BZ~Z7Sb8o2Hnzblr1Gu1MGgKtaigd~smLbhiBFeAUcMyu5g7a7ouTOBec2Ww__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":14193,"name":"Philosophy of Property","url":"https://www.academia.edu/Documents/in/Philosophy_of_Property"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"},{"id":288502,"name":"Jump","url":"https://www.academia.edu/Documents/in/Jump"}],"urls":[{"id":43687790,"url":"http://arxiv.org/pdf/2211.07527"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776046"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program"><img alt="Research paper thumbnail of Approximately low-rank recovery from noisy and local measurements by convex program" class="work-thumbnail" src="https://attachments.academia-assets.com/112088105/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program">Approximately low-rank recovery from noisy and local measurements by convex program</a></div><div class="wp-workCard_item"><span>Information and Inference: A Journal of the IMA</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Low-rank matrix models have been universally useful for numerous applications, from classical sys...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="493993c26ad12229407e601af568438f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088105,"asset_id":115776046,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776046"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776046"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776046; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776046]").text(description); $(".js-view-count[data-work-id=115776046]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776046; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776046']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776046, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "493993c26ad12229407e601af568438f" } } $('.js-work-strip[data-work-id=115776046]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776046,"title":"Approximately low-rank recovery from noisy and local measurements by convex program","translated_title":"","metadata":{"abstract":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","publisher":"Oxford University Press (OUP)","publication_name":"Information and Inference: A Journal of the IMA"},"translated_abstract":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","internal_url":"https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program","translated_internal_url":"","created_at":"2024-03-04T07:00:29.007-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088105,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088105/thumbnails/1.jpg","file_name":"2110.15205v1.pdf","download_url":"https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Approximately_low_rank_recovery_from_noi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088105/2110.15205v1-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DApproximately_low_rank_recovery_from_noi.pdf\u0026Expires=1733905078\u0026Signature=AWUzdhhDHvcVd~i92PXc5I566P9EO8Rzryzrojqt-q5isz1nOuUGkZeDbbN6C8X4iy6OgKVPL3EcxP9kfLMV~ZRLPy9sWhJtXtV0A0Hau9yy5izeSbzMOPNpTNgcdY9ZhLDwojW9uG7k~DoEjqXQA1ApCQxc54A~UNifjo-9ai0KupRc5679RqqBeBZHS6lGFhvDGrY91C2x8rfzMvfmIOwS6D1Mi8l~JK1Bp1kkZcUy1HX~8P-987pvdDjMQd5KGl4hbqXN8Bgjh2tG1HgvBKVkHEP3KV6OKgxH2QrFiKUGOM~RB3Mnt09~ny6RPRCJyZvKu6k~5IJidqjwBP3LmA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program","translated_slug":"","page_count":38,"language":"en","content_type":"Work","summary":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088105,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088105/thumbnails/1.jpg","file_name":"2110.15205v1.pdf","download_url":"https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Approximately_low_rank_recovery_from_noi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088105/2110.15205v1-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DApproximately_low_rank_recovery_from_noi.pdf\u0026Expires=1733905078\u0026Signature=AWUzdhhDHvcVd~i92PXc5I566P9EO8Rzryzrojqt-q5isz1nOuUGkZeDbbN6C8X4iy6OgKVPL3EcxP9kfLMV~ZRLPy9sWhJtXtV0A0Hau9yy5izeSbzMOPNpTNgcdY9ZhLDwojW9uG7k~DoEjqXQA1ApCQxc54A~UNifjo-9ai0KupRc5679RqqBeBZHS6lGFhvDGrY91C2x8rfzMvfmIOwS6D1Mi8l~JK1Bp1kkZcUy1HX~8P-987pvdDjMQd5KGl4hbqXN8Bgjh2tG1HgvBKVkHEP3KV6OKgxH2QrFiKUGOM~RB3Mnt09~ny6RPRCJyZvKu6k~5IJidqjwBP3LmA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":85880,"name":"Singular value decomposition","url":"https://www.academia.edu/Documents/in/Singular_value_decomposition"},{"id":95988,"name":"Matrix Completion","url":"https://www.academia.edu/Documents/in/Matrix_Completion"},{"id":806332,"name":"Estimator","url":"https://www.academia.edu/Documents/in/Estimator"},{"id":2720299,"name":"Matrix norm","url":"https://www.academia.edu/Documents/in/Matrix_norm"},{"id":4113180,"name":"operator norm","url":"https://www.academia.edu/Documents/in/operator_norm"}],"urls":[{"id":40025902,"url":"https://academic.oup.com/imaiai/article-pdf/12/3/1612/51602778/iaad013.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776045"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings"><img alt="Research paper thumbnail of Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings" class="work-thumbnail" src="https://attachments.academia-assets.com/112088106/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings">Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Trace inequalities are general techniques with many applications in quantum information theory, o...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="160efed2c7e1239e4fa8538231832a94" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088106,"asset_id":115776045,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776045"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776045"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776045; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776045]").text(description); $(".js-view-count[data-work-id=115776045]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776045; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776045']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776045, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "160efed2c7e1239e4fa8538231832a94" } } $('.js-work-strip[data-work-id=115776045]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776045,"title":"Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings","translated_title":"","metadata":{"abstract":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","publisher":"AIP Publishing","publication_name":"Journal of Mathematical Physics"},"translated_abstract":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","internal_url":"https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings","translated_internal_url":"","created_at":"2024-03-04T07:00:28.767-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088106,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088106/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Multivariate_trace_inequalities_p_fideli.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088106/2009-libre.pdf?1709564797=\u0026response-content-disposition=attachment%3B+filename%3DMultivariate_trace_inequalities_p_fideli.pdf\u0026Expires=1733905078\u0026Signature=aAjkaPt27v9QIElemeJspBV6Vd00GAEXKMAUhJAV70VVwRzZ3orfZJwmhF7Q7RiQwrZN~3XWjl4v0r45xpF7YfesOaw3DGmoKya8lgaorblQ40vPvkcq7VdrMn~8flMzxnXXQZFPcfc2GOZVsKt92fnmm3uGuNUZHQ6DfkQCpOARfJ8PqJN~Lr8zOuG8eYsUgiohRAsXv~XDqRZ6oUzN8E2SQVx0~UfEcWfeI92hMzsNCFtDBVePjKAdhi8j3m87rYgjnT4wV0F-gCneLx9eMrbO4yVnPOIhcBIqrQphoz87f6YPgIaJE9andd2zrkloKE4bDxQTqV8inSnYMgCzkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings","translated_slug":"","page_count":57,"language":"en","content_type":"Work","summary":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088106,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088106/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Multivariate_trace_inequalities_p_fideli.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088106/2009-libre.pdf?1709564797=\u0026response-content-disposition=attachment%3B+filename%3DMultivariate_trace_inequalities_p_fideli.pdf\u0026Expires=1733905078\u0026Signature=aAjkaPt27v9QIElemeJspBV6Vd00GAEXKMAUhJAV70VVwRzZ3orfZJwmhF7Q7RiQwrZN~3XWjl4v0r45xpF7YfesOaw3DGmoKya8lgaorblQ40vPvkcq7VdrMn~8flMzxnXXQZFPcfc2GOZVsKt92fnmm3uGuNUZHQ6DfkQCpOARfJ8PqJN~Lr8zOuG8eYsUgiohRAsXv~XDqRZ6oUzN8E2SQVx0~UfEcWfeI92hMzsNCFtDBVePjKAdhi8j3m87rYgjnT4wV0F-gCneLx9eMrbO4yVnPOIhcBIqrQphoz87f6YPgIaJE9andd2zrkloKE4bDxQTqV8inSnYMgCzkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":51108,"name":"Noncommutative Geometry","url":"https://www.academia.edu/Documents/in/Noncommutative_Geometry"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":403140,"name":"von Neumann algebra","url":"https://www.academia.edu/Documents/in/von_Neumann_algebra"},{"id":476286,"name":"Von Neumann Architecture","url":"https://www.academia.edu/Documents/in/Von_Neumann_Architecture"},{"id":2546925,"name":"von Neumann Entropy","url":"https://www.academia.edu/Documents/in/von_Neumann_Entropy"}],"urls":[{"id":40025901,"url":"https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0066653/16611663/122204_1_online.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776044"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure"><img alt="Research paper thumbnail of Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure" class="work-thumbnail" src="https://attachments.academia-assets.com/112088108/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure">Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure</a></div><div class="wp-workCard_item"><span>Journal of Statistical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroup...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint quantum Markov process can be used to prove estimates on the exponential convergence in relative entropy of quantum Markov systems which preserve a fixed state. This leads to estimates for the decay to equilibrium for coupled systems and to estimates for mixed state preparation times using Lindblad operators. Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1ebe2ac56fe2195348e371a73606793f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088108,"asset_id":115776044,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776044"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776044"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776044; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776044]").text(description); $(".js-view-count[data-work-id=115776044]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776044; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776044']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776044, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1ebe2ac56fe2195348e371a73606793f" } } $('.js-work-strip[data-work-id=115776044]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776044,"title":"Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. 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Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.","publication_name":"Journal of Statistical Physics","grobid_abstract_attachment_id":112088108},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure","translated_internal_url":"","created_at":"2024-03-04T07:00:28.524-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088108,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088108/thumbnails/1.jpg","file_name":"1911.pdf","download_url":"https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_of_Logarithmic_Sobolev_Inequal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088108/1911-libre.pdf?1709564783=\u0026response-content-disposition=attachment%3B+filename%3DStability_of_Logarithmic_Sobolev_Inequal.pdf\u0026Expires=1733905078\u0026Signature=NLdru2Xzk4u31gDP8F9yeoSfq8Reu-FqPcp9q1GNCDQs~DMKi26UyVxHuOpiLj~r7wfQ4L5ntIt0Lp5itE~6yaHEESFKNJYCowmsakLb5dqK21tLQlWmwguBGC0P8g892X2FtkyAPBmTHfRfvs12HU-BeBdR5Dmfgjx3c5xNuhvvuPNq48-hJ9DJm5OSYodDiiGcsxy1lJWMLcSP-guLK0rUeH~qceZhamxd-qP9nYmbXBYMORqcGY4qgRNb-WZMod1ymgk-TDLLx~ECxBmYNdJc1hoq-AxCGBXy2rDLhzqQRjn-01hqYPm5cWCsy64g4rwnKx46TlA2b1Y2ZV8wVQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure","translated_slug":"","page_count":26,"language":"en","content_type":"Work","summary":"We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint quantum Markov process can be used to prove estimates on the exponential convergence in relative entropy of quantum Markov systems which preserve a fixed state. This leads to estimates for the decay to equilibrium for coupled systems and to estimates for mixed state preparation times using Lindblad operators. Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088108,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088108/thumbnails/1.jpg","file_name":"1911.pdf","download_url":"https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_of_Logarithmic_Sobolev_Inequal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088108/1911-libre.pdf?1709564783=\u0026response-content-disposition=attachment%3B+filename%3DStability_of_Logarithmic_Sobolev_Inequal.pdf\u0026Expires=1733905078\u0026Signature=NLdru2Xzk4u31gDP8F9yeoSfq8Reu-FqPcp9q1GNCDQs~DMKi26UyVxHuOpiLj~r7wfQ4L5ntIt0Lp5itE~6yaHEESFKNJYCowmsakLb5dqK21tLQlWmwguBGC0P8g892X2FtkyAPBmTHfRfvs12HU-BeBdR5Dmfgjx3c5xNuhvvuPNq48-hJ9DJm5OSYodDiiGcsxy1lJWMLcSP-guLK0rUeH~qceZhamxd-qP9nYmbXBYMORqcGY4qgRNb-WZMod1ymgk-TDLLx~ECxBmYNdJc1hoq-AxCGBXy2rDLhzqQRjn-01hqYPm5cWCsy64g4rwnKx46TlA2b1Y2ZV8wVQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":16460,"name":"Statistical Physics","url":"https://www.academia.edu/Documents/in/Statistical_Physics"},{"id":51108,"name":"Noncommutative Geometry","url":"https://www.academia.edu/Documents/in/Noncommutative_Geometry"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":595993,"name":"Markov chain","url":"https://www.academia.edu/Documents/in/Markov_chain"},{"id":741671,"name":"Markov Process","url":"https://www.academia.edu/Documents/in/Markov_Process"},{"id":3193313,"name":"arXiv","url":"https://www.academia.edu/Documents/in/arXiv"},{"id":3292545,"name":"Logarithm","url":"https://www.academia.edu/Documents/in/Logarithm"}],"urls":[{"id":40025900,"url":"https://link.springer.com/content/pdf/10.1007/s10955-022-03026-x.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776043"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games"><img alt="Research paper thumbnail of On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games" class="work-thumbnail" src="https://attachments.academia-assets.com/112088099/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games">On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this work we show that, given a linear map from a general operator space into the dual of a C ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="31f2d837dc38193bea74f4439e19b3db" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088099,"asset_id":115776043,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776043"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776043"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776043; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776043]").text(description); $(".js-view-count[data-work-id=115776043]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776043; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776043']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776043, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "31f2d837dc38193bea74f4439e19b3db" } } $('.js-work-strip[data-work-id=115776043]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776043,"title":"On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.","publication_name":"Journal of Functional Analysis","grobid_abstract_attachment_id":112088099},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games","translated_internal_url":"","created_at":"2024-03-04T07:00:28.276-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088099/thumbnails/1.jpg","file_name":"2112.05214v1.pdf","download_url":"https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_the_relation_between_completely_bound.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088099/2112.05214v1-libre.pdf?1709564781=\u0026response-content-disposition=attachment%3B+filename%3DOn_the_relation_between_completely_bound.pdf\u0026Expires=1733905078\u0026Signature=RQzLzcve4AWr8l8UmD5UOG97-ekR0B1wXlbGolNF1r~Bh8t8VGRHTSU43rSabCz9zXKFFFvLUL4lZubQ4ZQGHcQ5rGFeNA4ruF3W6Mt5GrMgFD3ftqmMR2ruQ7PpC-NLo~60HKl5UGY9S5-PPBz21QuKAlzMPVz3mGkpLHITVMbgQ6eJBGvFUcCTupAIp-C7BtKgkafPGTu7IY9427WaH6wSb0oydM1MRwG5fJLM7ALGIQf263BMTM0B4BQkiOqUTTJlik2J~Lz~TYsSC1PJNbe2uBc-bHilnN~k1b7mNZmJwqzv0UtnC8xrcTIfpXbCpDbS5b3y~LRE~x1L5LKhTA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games","translated_slug":"","page_count":23,"language":"en","content_type":"Work","summary":"In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088099/thumbnails/1.jpg","file_name":"2112.05214v1.pdf","download_url":"https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_the_relation_between_completely_bound.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088099/2112.05214v1-libre.pdf?1709564781=\u0026response-content-disposition=attachment%3B+filename%3DOn_the_relation_between_completely_bound.pdf\u0026Expires=1733905078\u0026Signature=RQzLzcve4AWr8l8UmD5UOG97-ekR0B1wXlbGolNF1r~Bh8t8VGRHTSU43rSabCz9zXKFFFvLUL4lZubQ4ZQGHcQ5rGFeNA4ruF3W6Mt5GrMgFD3ftqmMR2ruQ7PpC-NLo~60HKl5UGY9S5-PPBz21QuKAlzMPVz3mGkpLHITVMbgQ6eJBGvFUcCTupAIp-C7BtKgkafPGTu7IY9427WaH6wSb0oydM1MRwG5fJLM7ALGIQf263BMTM0B4BQkiOqUTTJlik2J~Lz~TYsSC1PJNbe2uBc-bHilnN~k1b7mNZmJwqzv0UtnC8xrcTIfpXbCpDbS5b3y~LRE~x1L5LKhTA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"}],"urls":[{"id":40025899,"url":"https://api.elsevier.com/content/article/PII:S0022123622003287?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776042"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel"><img alt="Research paper thumbnail of The Communication Value of a Quantum Channel" class="work-thumbnail" src="https://attachments.academia-assets.com/112088098/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel">The Communication Value of a Quantum Channel</a></div><div class="wp-workCard_item"><span>2022 IEEE International Symposium on Information Theory (ISIT)</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">There are various ways to quantify the communication capabilities of a quantum channel. In this w...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4c34c78d284e4b2257b7f87b239cf598" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088098,"asset_id":115776042,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776042"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776042"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776042; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776042]").text(description); $(".js-view-count[data-work-id=115776042]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776042; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776042']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776042, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4c34c78d284e4b2257b7f87b239cf598" } } $('.js-work-strip[data-work-id=115776042]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776042,"title":"The Communication Value of a Quantum Channel","translated_title":"","metadata":{"publisher":"IEEE","grobid_abstract":"There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.","publication_name":"2022 IEEE International Symposium on Information Theory (ISIT)","grobid_abstract_attachment_id":112088098},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel","translated_internal_url":"","created_at":"2024-03-04T07:00:28.022-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088098/thumbnails/1.jpg","file_name":"2109.11144v1.pdf","download_url":"https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_Communication_Value_of_a_Quantum_Cha.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088098/2109.11144v1-libre.pdf?1709564793=\u0026response-content-disposition=attachment%3B+filename%3DThe_Communication_Value_of_a_Quantum_Cha.pdf\u0026Expires=1733905078\u0026Signature=Bs59dhxY2XO5ErQlF8Ng8juDBF5Vg9-C1XdKgJ7YgAuXjDEeVmDNEEKMOsNO7c6uqhF5UGd~ujzRpyDoVm1qsbnVCoHym00FL5Am6f3BIlxJksuWYnqgMXmcqKG5dCs3vaD5OoRRVbmTg-Y8zCU9RV-jQoT1eHrqUVuWc4unUsJB~egEmIUphlCxcJyn4Q5h-nJ5ZhRftuLoR2Hp9uaoWf-TpHqrQfK3Lbyy~JJBlb7BkD~E1xNG4UUZHUXuHV47Vw0KfdqNEpILY-wRXziGkwL3-aNp4qpADmlq7wCInop4Jih6r-F-XhB6j8d6CMBP825zqB-sRK2BDwtkzwC2Sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_Communication_Value_of_a_Quantum_Channel","translated_slug":"","page_count":21,"language":"en","content_type":"Work","summary":"There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088098/thumbnails/1.jpg","file_name":"2109.11144v1.pdf","download_url":"https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_Communication_Value_of_a_Quantum_Cha.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088098/2109.11144v1-libre.pdf?1709564793=\u0026response-content-disposition=attachment%3B+filename%3DThe_Communication_Value_of_a_Quantum_Cha.pdf\u0026Expires=1733905078\u0026Signature=Bs59dhxY2XO5ErQlF8Ng8juDBF5Vg9-C1XdKgJ7YgAuXjDEeVmDNEEKMOsNO7c6uqhF5UGd~ujzRpyDoVm1qsbnVCoHym00FL5Am6f3BIlxJksuWYnqgMXmcqKG5dCs3vaD5OoRRVbmTg-Y8zCU9RV-jQoT1eHrqUVuWc4unUsJB~egEmIUphlCxcJyn4Q5h-nJ5ZhRftuLoR2Hp9uaoWf-TpHqrQfK3Lbyy~JJBlb7BkD~E1xNG4UUZHUXuHV47Vw0KfdqNEpILY-wRXziGkwL3-aNp4qpADmlq7wCInop4Jih6r-F-XhB6j8d6CMBP825zqB-sRK2BDwtkzwC2Sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":43591,"name":"Quantum entanglement","url":"https://www.academia.edu/Documents/in/Quantum_entanglement"},{"id":4027512,"name":"Quantum Channel","url":"https://www.academia.edu/Documents/in/Quantum_Channel"}],"urls":[{"id":40025898,"url":"http://xplorestaging.ieee.org/ielx7/9834325/9834269/09834380.pdf?arnumber=9834380"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776041"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776041/q_Chaos"><img alt="Research paper thumbnail of q-Chaos" class="work-thumbnail" src="https://attachments.academia-assets.com/112088025/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776041/q_Chaos">q-Chaos</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1)...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1&lt;q&lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d11989a6ee53becec35f85a5efbcf3e7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088025,"asset_id":115776041,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776041"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776041"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776041; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776041]").text(description); $(".js-view-count[data-work-id=115776041]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776041; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776041']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776041, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d11989a6ee53becec35f85a5efbcf3e7" } } $('.js-work-strip[data-work-id=115776041]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776041,"title":"q-Chaos","translated_title":"","metadata":{"abstract":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","publication_date":{"day":24,"month":1,"year":2008,"errors":{}}},"translated_abstract":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","internal_url":"https://www.academia.edu/115776041/q_Chaos","translated_internal_url":"","created_at":"2024-03-04T07:00:27.792-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088025,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088025/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088025/0801.3704v1-libre.pdf?1709564790=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=aSPHr4ylsRcdO0VXxunjwgE1mpMWAvJhC0TEuchL7lgnQRXsmCuodMw~dY-yMQt0cGFUJwkBX~2N6H~~y-EiI4a5PjKcq9G5kBS9SGl1vVTuiW1h0CVesBwc89SxZ2MDnEyj7bezfMtW8EYfxxjRP12~T0fBON9GSoCnjQVIA~etLatdC3HFJmEhN4JCBmRdcLXr0SsR6-SEC7Dw1VSgZxhIZp0js~yUqDOWp7nfWw6hiuM844wKBYoul4h9WlRMKTOrBBz1zOfZ65uMUAdHQjTlLI3~3o3OaIQmTAxahAeQT7uGNNxC~IIKmymwmSz-5nmsuhX5-zKIcyjaPOmOkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"q_Chaos","translated_slug":"","page_count":22,"language":"en","content_type":"Work","summary":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088025,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088025/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088025/0801.3704v1-libre.pdf?1709564790=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=aSPHr4ylsRcdO0VXxunjwgE1mpMWAvJhC0TEuchL7lgnQRXsmCuodMw~dY-yMQt0cGFUJwkBX~2N6H~~y-EiI4a5PjKcq9G5kBS9SGl1vVTuiW1h0CVesBwc89SxZ2MDnEyj7bezfMtW8EYfxxjRP12~T0fBON9GSoCnjQVIA~etLatdC3HFJmEhN4JCBmRdcLXr0SsR6-SEC7Dw1VSgZxhIZp0js~yUqDOWp7nfWw6hiuM844wKBYoul4h9WlRMKTOrBBz1zOfZ65uMUAdHQjTlLI3~3o3OaIQmTAxahAeQT7uGNNxC~IIKmymwmSz-5nmsuhX5-zKIcyjaPOmOkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088024,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088024/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088024/download_file","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088024/0801.3704v1-libre.pdf?1709564780=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=NOmyxr-S86jVkXCDcnddcpfdrpQ4Es9RTSQ3nlnQCS4USVphJzkgtJFnpklxGFn5tHHctU8HqJoixTaxbTqQoxJMpAsQK-bbESc9nZYjOhr6afYeuOgINdjGMu-rFqZQX-gzEEZOrl7CLvDTyUvGO49fRbXi64dr-M7lah8-zRcCK0oT5rQScpuqTiv4GZvXVgXnPmDAIKMzKD2yL54TJ9FJMFvZfkm2wZ7KMtFK0C8NHIrH9rLKoQN1xeZb1~3ZNqAplNSmzBtiIN4xqAF6jDAuFDFBloriA8P4yC7LBy~RsrrsOa0u2dPx81dDevR6DmTbrZkPxCk7kdDnxjjNGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":40025897,"url":"https://arxiv.org/pdf/0801.3704v1.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776040"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776040/Associated_with_Semigroups"><img alt="Research paper thumbnail of Associated with Semigroups" class="work-thumbnail" src="https://attachments.academia-assets.com/112088023/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776040/Associated_with_Semigroups">Associated with Semigroups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This article is an introduction to our recent work in harmonic analysis associated with semigroup...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calderón-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics-or with very little information on the metric-Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting but it is also valid in classical/commutative frameworks.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fda1e07e6dbf76ec5cefe54fcd7bf1a4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088023,"asset_id":115776040,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088023/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776040"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776040"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776040; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776040]").text(description); $(".js-view-count[data-work-id=115776040]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776040; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776040']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776040, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "fda1e07e6dbf76ec5cefe54fcd7bf1a4" } } $('.js-work-strip[data-work-id=115776040]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776040,"title":"Associated with Semigroups","translated_title":"","metadata":{"grobid_abstract":"This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calderón-Zygmund theory for von Neumann algebras. 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The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics-or with very little information on the metric-Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting but it is also valid in classical/commutative frameworks.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088023,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088023/thumbnails/1.jpg","file_name":"download.pdf","download_url":"https://www.academia.edu/attachments/112088023/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Associated_with_Semigroups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088023/download-libre.pdf?1709564785=\u0026response-content-disposition=attachment%3B+filename%3DAssociated_with_Semigroups.pdf\u0026Expires=1733905078\u0026Signature=MPfsGu6KtQyyaU2Tb~cyPsiMmYHNELOLASQ3GON~X9T1x4MycIp3uoVq~SlUqFNYsAAzqW~B2jud9TQzZJ8f7DMXSmH2T0I4nD2hXbx4Q5Yks~6aAKAPhDpqU5qt7AL2ih6ou00gBPeW~haYIUIIiEdZy5woyeJE9E1irH-nbxL9TsgZLOWdWBAeFE-qwGU2MmAhQGTq5E6Vd7vi9H7Oc79OvkFvSo25L5z9t5LZn~9XrL2pvV-K1YrAzG2nH3WVcskhoKXWbxzEyREr9uWz0x0ea38G-3~Wb6xetDGU46jCB24O2UxUNuTt45o78irygZCzMxtyDAKEs3QJD2hcNA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088022,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088022/thumbnails/1.jpg","file_name":"download.pdf","download_url":"https://www.academia.edu/attachments/112088022/download_file","bulk_download_file_name":"Associated_with_Semigroups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088022/download-libre.pdf?1709564781=\u0026response-content-disposition=attachment%3B+filename%3DAssociated_with_Semigroups.pdf\u0026Expires=1733905078\u0026Signature=KJs-8~xiVIiz90ZqwCAat8M7FAQAkkoaD-UIcDxuJzneY7uLpzVbf8SwZvOljYkLo3iWUy0126cE19nzLeXj7PRHkzWSwRzpOczYcgvnfZoYKOEbZL~54d0UmjIAe2hKNwUx5L50MLAGwyD54qgE0JqPIUKFj5EThMsk5Zs~yZBuDptJSWb0fpdGqO75aEyUj~WUDsNvl~lZxwxay0ZaBwAaoQi0UC6cbioxkJCn-sKozaTnVKpxzLvYQqtqiCKsazp2CDpHSbUS02OkkHpB7cImiSHAFPD0a8UDyPHtDfNFDx43A13P7-NIshM69wOwGRvVZxcjav3Txe6YADoqSA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":40025896,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.830.6373\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776039"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776039/Theory_of_Amalgamated"><img alt="Research paper thumbnail of Theory of Amalgamated" class="work-thumbnail" src="https://attachments.academia-assets.com/112088092/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776039/Theory_of_Amalgamated">Theory of Amalgamated</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let f1, f2,..., fn be a family of independent copies of a given random variable f in a probabilit...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let f1, f2,..., fn be a family of independent copies of a given random variable f in a probability space (Ω, F, µ). Then, the following equivalence of norms holds whenever 1 ≤ q ≤ p &lt; ∞ (Σpq)</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4d2091b0bebf7fce4270bdf2ed46a0c1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088092,"asset_id":115776039,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088092/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776039"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776039"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776039; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776039]").text(description); $(".js-view-count[data-work-id=115776039]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776039; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776039']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776039, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4d2091b0bebf7fce4270bdf2ed46a0c1" } } $('.js-work-strip[data-work-id=115776039]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776039,"title":"Theory of Amalgamated","translated_title":"","metadata":{"abstract":"Let f1, f2,..., fn be a family of independent copies of a given random variable f in a probability space (Ω, F, µ). 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Then, the following equivalence of norms holds whenever 1 ≤ q ≤ p &lt; ∞ (Σpq)</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b6950e0f9eb4f98e6f53d448fa1c472d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088093,"asset_id":115776037,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088093/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776037"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776037"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776037; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776037]").text(description); $(".js-view-count[data-work-id=115776037]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776037; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776037']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776037, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b6950e0f9eb4f98e6f53d448fa1c472d" } } $('.js-work-strip[data-work-id=115776037]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776037,"title":"Theory of Amalgamated","translated_title":"","metadata":{"abstract":"Let f1, f2,..., fn be a family of independent copies of a given random variable f in a probability space (Ω, F, µ). 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Then, the following equivalence of norms holds whenever 1 ≤ q ≤ p \u0026lt; ∞ (Σpq)","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088093/thumbnails/1.jpg","file_name":"0511406v2.pdf","download_url":"https://www.academia.edu/attachments/112088093/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_Amalgamated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088093/0511406v2-libre.pdf?1709564891=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_Amalgamated.pdf\u0026Expires=1733905078\u0026Signature=GG0nnPyy6SVUNMD903oMyqQXVt3~AaJ-bfxi6XfpQY9xneEruBXWSuMlMUm77OP-PAfcLSVcbYtmw2FgDvyLRywOTBW50sJka~0hnsS0Eq8fQsTyz6Tmrt77t7ZpaDJAXpUfP9uuz3~CRxKFGG6WROA4GHptZfBWTvWTmPEG0hEBYlzi-Vrou4sz~c1-uMf~RQrRPmswC9cheeFr169WXYlP1q2Q~oamlSDTdGoEQIBtDPkFwgn4Akhm64PPpDMTjSLA3FXavycUDe9KTYmztQNdOhp7d2H-lxXjxfwnNDj0LZ4Cx~QnSKyXsF2xcptGLGgbxJaCjFUxNaEl8EsrNg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":40025894,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.241.3266\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776036"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras"><img alt="Research paper thumbnail of Ultraproduct methods for mixed $q$-Gaussian algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112088020/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras">Ultraproduct methods for mixed $q$-Gaussian algebras</a></div><div class="wp-workCard_item"><span>arXiv: Operator Algebras</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian alge...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\delta_{ij}$. Here we also allow equality in $-1\le q_{ij}=q_{ji}\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher&#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\&#39;e inequalities with constants $C\sqrt{p}$.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e5b14f8ea4427f83a4c293c1ea5cdfa0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088020,"asset_id":115776036,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776036"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776036"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776036; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776036]").text(description); $(".js-view-count[data-work-id=115776036]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776036; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776036']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776036, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e5b14f8ea4427f83a4c293c1ea5cdfa0" } } $('.js-work-strip[data-work-id=115776036]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776036,"title":"Ultraproduct methods for mixed $q$-Gaussian algebras","translated_title":"","metadata":{"abstract":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","ai_title_tag":"Unified Ultraproduct Approach for Mixed q-Gaussian Algebras","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"arXiv: Operator Algebras"},"translated_abstract":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","internal_url":"https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras","translated_internal_url":"","created_at":"2024-03-04T07:00:26.374-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088020,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088020/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088020/1505.07852v2-libre.pdf?1709564801=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=XGM3HZ9iGbbV-q5Ph~~FVQfwj09~w2whbaGIf8whJwy1yZAOy5Mm690xY4MsA3gcaSDnVVBbQ~Kt~L4ZbREXvCCIM0J7d5w1C2NgmQr0CBWIbMvbn2QSiGNj4ftkQvnZOkEc8JzPf-yLRlMq91JleG1ySiAbKsSUZtq86Mz8D-2zf5xoValm6yUImKZn4hH~e1t0j-VeYhQXzL-1I8f1QfemwLXdfkbd1fWydKw9TzSwK8xAraNEAtYrcl028-aI97ai0yFXGO94Sd4sAgyZ-FaX~VXw--AzOyhe6shNcgg5Po-6JRRCk~AqCQf1rdkMxAFpCIbIuaCq9XR3uaGSxg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Ultraproduct_methods_for_mixed_q_Gaussian_algebras","translated_slug":"","page_count":47,"language":"en","content_type":"Work","summary":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088020,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088020/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088020/1505.07852v2-libre.pdf?1709564801=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=XGM3HZ9iGbbV-q5Ph~~FVQfwj09~w2whbaGIf8whJwy1yZAOy5Mm690xY4MsA3gcaSDnVVBbQ~Kt~L4ZbREXvCCIM0J7d5w1C2NgmQr0CBWIbMvbn2QSiGNj4ftkQvnZOkEc8JzPf-yLRlMq91JleG1ySiAbKsSUZtq86Mz8D-2zf5xoValm6yUImKZn4hH~e1t0j-VeYhQXzL-1I8f1QfemwLXdfkbd1fWydKw9TzSwK8xAraNEAtYrcl028-aI97ai0yFXGO94Sd4sAgyZ-FaX~VXw--AzOyhe6shNcgg5Po-6JRRCk~AqCQf1rdkMxAFpCIbIuaCq9XR3uaGSxg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088021,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088021/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088021/download_file","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088021/1505.07852v2-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=ZKIGhZ9nFaJsjepIbvxDQe7q8~Quv4BOQsRYOu9Ii2VVDaUxhmODs0Iway1JMQuqfZLrEZ1p8BOv~wSnmu7PZK4UOO~-snxegILphpHyxx3Tyz~L44iuFCBtd9VrhAbrBXhXXB34lqhiSLRjTe4HkJB6VvBcy7fF8MwWEAl76CaltPbLobL54XWP2bJL05rCOqz07g-J1sKMv2U7e21nsiW51p6Lo-9rc0oXs9UYQI4J4UYKX-ymBqoJwxZ56uyjZYBjfhH-u0TaJKdohjk-Z5zS4tlnLx-9voKyhs2OV7OuUqmbs4OGlZOsEQ9sHxl67CBq68Pb3WwTBZDxcBVRkA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":342314,"name":"Gaussian","url":"https://www.academia.edu/Documents/in/Gaussian"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":40025893,"url":"https://arxiv.org/pdf/1505.07852v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776035"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776035/Universal_recovery_and_p_fidelity_in_von_Neumann_algebras"><img alt="Research paper thumbnail of Universal recovery and p-fidelity in von Neumann algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112088018/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776035/Universal_recovery_and_p_fidelity_in_von_Neumann_algebras">Universal recovery and p-fidelity in von Neumann algebras</a></div><div class="wp-workCard_item"><span>arXiv: Quantum Physics</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Scenarios ranging from quantum error correction to high energy physics use recovery maps, which t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. This technique has many potential applications in porting results from quantum information theory to...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3775c8a2cfc9821643cf25060141286f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088018,"asset_id":115776035,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088018/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776035"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776035"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776035; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776035]").text(description); $(".js-view-count[data-work-id=115776035]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776035; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776035']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776035, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "3775c8a2cfc9821643cf25060141286f" } } $('.js-work-strip[data-work-id=115776035]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776035,"title":"Universal recovery and p-fidelity in von Neumann algebras","translated_title":"","metadata":{"abstract":"Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. This technique has many potential applications in porting results from quantum information theory to...","publication_date":{"day":null,"month":null,"year":2020,"errors":{}},"publication_name":"arXiv: Quantum Physics"},"translated_abstract":"Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. 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The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. This technique has many potential applications in porting results from quantum information theory to...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088018,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088018/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088018/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Universal_recovery_and_p_fidelity_in_von.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088018/2009-libre.pdf?1709564788=\u0026response-content-disposition=attachment%3B+filename%3DUniversal_recovery_and_p_fidelity_in_von.pdf\u0026Expires=1733905078\u0026Signature=FiTNFq7~izscsxdTVGCPqUCXQHIEgtQSg7G6U5mNzDnufgPz59GxV53gLMD4TMQ89OOTIUXd8MEMTxEMtwvEEtQvyTozMoEAfLmFx5~ElJELxSdoHgKomvGzhGzs~opn4MB8Tk~9gR07QJiA3Oc2bq4rRvrCxazoTGU5DEgtcx3EzCueRp4JW71bozROtNaunDgfTCXKiy89aNqll4W0gPgKyJpDPEJbNPugDzhj1njSdZ30uQzD9CXzLScHGzcveMZwAjS670Ue-Z144avq~YIoWpW~l25dOV1GdR99OO1KeW4PBvbwvOXFnOv0Tsu59DxM9ujXU1POl2-hdZjWQw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088019,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088019/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088019/download_file","bulk_download_file_name":"Universal_recovery_and_p_fidelity_in_von.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088019/2009-libre.pdf?1709564806=\u0026response-content-disposition=attachment%3B+filename%3DUniversal_recovery_and_p_fidelity_in_von.pdf\u0026Expires=1733905078\u0026Signature=IhJZ87XXrTpMxLTZQt2MSRLgqtYTyEaRKEa9RLvTJjEkWsTaX~f0EkixBMiBIOQYK6o9zN6ORYrw9TPrsmusGlFA99s8-ItjtMj2LKcnIJ8XGf4XKk5ryVypKL0JT3exF0Vum0098TZ2o74llMpYleocOS8UqfBcSQcuXYv0cMHW5EOiSkVUC5CMZ8gKYjCWXtECTxtbDnw0V~jZQmaDTVB-W8ZZMRn85r83xUB~lNMZQjOLr~iPuo2RY9ZDTpi3Mz1PAy4YlMxR7BFNKdtlD7XWNIEv3kQH9XFaUcxpEsn9CT60Y4qd7L9TCwxlFp9lAnUN3bMt8jkbPgNg0S198A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"},{"id":403140,"name":"von Neumann algebra","url":"https://www.academia.edu/Documents/in/von_Neumann_algebra"},{"id":476286,"name":"Von Neumann Architecture","url":"https://www.academia.edu/Documents/in/Von_Neumann_Architecture"},{"id":2546925,"name":"von Neumann Entropy","url":"https://www.academia.edu/Documents/in/von_Neumann_Entropy"},{"id":2628777,"name":"Kullback-Leibler divergence","url":"https://www.academia.edu/Documents/in/Kullback-Leibler_divergence"},{"id":3292545,"name":"Logarithm","url":"https://www.academia.edu/Documents/in/Logarithm"}],"urls":[{"id":40025892,"url":"http://export.arxiv.org/pdf/2009.11866"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="12034261" id="papers"><div class="js-work-strip profile--work_container" data-work-id="122354538"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates"><img alt="Research paper thumbnail of Complete order and relative entropy decay rates" class="work-thumbnail" src="https://attachments.academia-assets.com/117036703/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates">Complete order and relative entropy decay rates</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Sep 22, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for matrix-valued functions. For quantum Markov semigroups, we obtain that the complete modified logarithmic Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension constant. This estimate is asymptotically tight for a quantum birth-death process. Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6c59821c686a55f86ef98054975c1001" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036703,"asset_id":122354538,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354538"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354538"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354538; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354538]").text(description); $(".js-view-count[data-work-id=122354538]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354538; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354538']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354538, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6c59821c686a55f86ef98054975c1001" } } $('.js-work-strip[data-work-id=122354538]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354538,"title":"Complete order and relative entropy decay rates","translated_title":"","metadata":{"publisher":"Cornell University","grobid_abstract":"We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for matrix-valued functions. For quantum Markov semigroups, we obtain that the complete modified logarithmic Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension constant. This estimate is asymptotically tight for a quantum birth-death process. Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.","publication_date":{"day":22,"month":9,"year":2022,"errors":{}},"publication_name":"arXiv (Cornell University)","grobid_abstract_attachment_id":117036703},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354538/Complete_order_and_relative_entropy_decay_rates","translated_internal_url":"","created_at":"2024-07-25T22:49:34.902-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036703,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036703/thumbnails/1.jpg","file_name":"2209.pdf","download_url":"https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Complete_order_and_relative_entropy_deca.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036703/2209-libre.pdf?1721973196=\u0026response-content-disposition=attachment%3B+filename%3DComplete_order_and_relative_entropy_deca.pdf\u0026Expires=1733905077\u0026Signature=Aqcm5kGtNFhyK0MkK9xiY2rMnnMfUSEGUN9gdH4kmbRdIG-qAJcqgHVeiGpPtUrCUTeSj-bYh10RyUKk6cwYA0Pq0nzfHM2dDFHcuRMkashe1UOBfzRnzLsCAbua4Wh5bPXo1R1eBb5L16oIvII7lQCu2nia6oNSHH5sre29lu7OlIm8hxYlN7JrXPof4C-RVYajubj~9pilseo2Y3aa-vfktpPvdd6EuL08OSc5eNuhe6CSW5kH6j3tDFX5j4NsDlYnCFU3veZ7EB3D-W9aiDnoyEUh797KIw~yIxZv8N1h7cdxNVSdLaZzfj8DybgLizrlA-vrc~diK3bbRfKJyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Complete_order_and_relative_entropy_decay_rates","translated_slug":"","page_count":58,"language":"en","content_type":"Work","summary":"We prove that the complete modified logarithmic Sobolev constant of a quantum Markov semigroup is bounded by the inverse of its complete positivity mixing time. For classical Markov semigroups, this implies that every sub-Laplacian given by a Hörmander system on a compact manifold satisfies a uniform modified log-Sobolev inequality for matrix-valued functions. For quantum Markov semigroups, we obtain that the complete modified logarithmic Sobolev constant is comparable to spectral gap up to a constant as logarithm of dimension constant. This estimate is asymptotically tight for a quantum birth-death process. Our results and the consequence of concentration inequalities apply to GNS-symmetric semigroups on general von Neumann algebras.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117036703,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036703/thumbnails/1.jpg","file_name":"2209.pdf","download_url":"https://www.academia.edu/attachments/117036703/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Complete_order_and_relative_entropy_deca.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036703/2209-libre.pdf?1721973196=\u0026response-content-disposition=attachment%3B+filename%3DComplete_order_and_relative_entropy_deca.pdf\u0026Expires=1733905077\u0026Signature=Aqcm5kGtNFhyK0MkK9xiY2rMnnMfUSEGUN9gdH4kmbRdIG-qAJcqgHVeiGpPtUrCUTeSj-bYh10RyUKk6cwYA0Pq0nzfHM2dDFHcuRMkashe1UOBfzRnzLsCAbua4Wh5bPXo1R1eBb5L16oIvII7lQCu2nia6oNSHH5sre29lu7OlIm8hxYlN7JrXPof4C-RVYajubj~9pilseo2Y3aa-vfktpPvdd6EuL08OSc5eNuhe6CSW5kH6j3tDFX5j4NsDlYnCFU3veZ7EB3D-W9aiDnoyEUh797KIw~yIxZv8N1h7cdxNVSdLaZzfj8DybgLizrlA-vrc~diK3bbRfKJyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":43689367,"url":"http://arxiv.org/pdf/2209.11684"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122354532"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354532/q_Chaos"><img alt="Research paper thumbnail of 𝑞-Chaos" class="work-thumbnail" src="https://attachments.academia-assets.com/117036704/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354532/q_Chaos">𝑞-Chaos</a></div><div class="wp-workCard_item"><span>Transactions of the American Mathematical Society</span><span>, May 18, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 < q < 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b3cab1d49d142b1ff2d6de13493bbd61" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036704,"asset_id":122354532,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036704/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354532"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354532"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354532; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354532]").text(description); $(".js-view-count[data-work-id=122354532]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354532; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354532']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354532, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b3cab1d49d142b1ff2d6de13493bbd61" } } $('.js-work-strip[data-work-id=122354532]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354532,"title":"𝑞-Chaos","translated_title":"","metadata":{"publisher":"American Mathematical Society","grobid_abstract":"We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 \u003c q \u003c 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.","publication_date":{"day":18,"month":5,"year":2011,"errors":{}},"publication_name":"Transactions of the American Mathematical Society","grobid_abstract_attachment_id":117036704},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354532/q_Chaos","translated_internal_url":"","created_at":"2024-07-25T22:49:34.019-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036704,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036704/thumbnails/1.jpg","file_name":"S0002-9947-2011-05165-2.pdf","download_url":"https://www.academia.edu/attachments/117036704/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036704/S0002-9947-2011-05165-2-libre.pdf?1721973185=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905077\u0026Signature=DosZsLkWcq8S6HFpv6PXQTWfeJ2OX8TzsX6cuZX9S5JvZBksYjPdEYE6W3DsfF0oeLQmi-vMJ0jaq9bqlX1KjQCnU6gU8SjH~whOQZ66ljTE1tOg2UE8A8ZzcSW3MVXBP5Rj~xsKX~bqP1ee7VXiIoqKv3ia8m5f8ORilYEg2h0QF~IAjlAIHE9fak8UoXFLI4KQbG~Gk1ZUNeXswWS~kfcYun-hVjvi1ZfoQZY2JfatsyZlnlSkmuEM7vw1LoAqGLUbuGAAAMr6yj8uWDtrssMzIQWBvuDdNQMt0ReJsAyLuL86~4NsfjINfXPhpIBdNiR~DSp-5f8Fy7gQguuADg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"q_Chaos","translated_slug":"","page_count":27,"language":"en","content_type":"Work","summary":"We consider the L p norm estimates for homogeneous polynomials of q-Gaussian variables (−1 ≤ q ≤ 1). When −1 \u003c q \u003c 1 the L p estimates for 1 ≤ p ≤ 2 are essentially the same as the free case (q = 0), whilst the L p estimates for 2 ≤ p ≤ ∞ show a strong q-dependence. Moreover, the extremal cases q = ±1 produce decisively different formulae.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius 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/></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354528/Relative_Embeddability_of_von_Neumann_Algebras_and_Amalgamated_Free_Products">Relative Embeddability of von Neumann Algebras and Amalgamated Free Products</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Dec 14, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ⊆ M , we have the reduced amalgamated free product * N M is embeddable into (R⊗N 1) ω for some other finite von Neumann algebra N 1 , where R is the hyperfinite II 1 factor.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="957c3cb7dc71ca94803fe53f9ad07c67" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036699,"asset_id":122354528,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036699/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" 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University)","grobid_abstract_attachment_id":117036699},"translated_abstract":null,"internal_url":"https://www.academia.edu/122354528/Relative_Embeddability_of_von_Neumann_Algebras_and_Amalgamated_Free_Products","translated_internal_url":"","created_at":"2024-07-25T22:49:33.325-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036699,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036699/thumbnails/1.jpg","file_name":"2012.pdf","download_url":"https://www.academia.edu/attachments/117036699/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Relative_Embeddability_of_von_Neumann_Al.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036699/2012-libre.pdf?1721973195=\u0026response-content-disposition=attachment%3B+filename%3DRelative_Embeddability_of_von_Neumann_Al.pdf\u0026Expires=1733905077\u0026Signature=EmDKNQrQQupAeFNs0THZ6eRbZmwWssbHMuzxE7oWVhhoqbH1VQBRB-TM3Xq-Ll~uudDf~jM6XLfcf5JNoQTwWr~91XKdq4DSpQNzSYitDBnzyoqzCQyszdQpIo113KMYjWtfLANFpzHxN4iVwzOt4q1DDjIjLPmJ-U-0WgDjLDgHd9veh91IoHag5ziUo6NPWzO1eYfgMuNlH~Ez-eLZmS4blNl~OOCDztULhtgsZvAQgJIZmivnPLnjYZJoCG1K1i-j~eQ4UuygcVGU~kXfDj3wKARXLn54tz10OZ8W0rcwxzDQxn2yWSMCylJZtn538GKQzZwPlntbpYa-DdPCXg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Relative_Embeddability_of_von_Neumann_Algebras_and_Amalgamated_Free_Products","translated_slug":"","page_count":36,"language":"en","content_type":"Work","summary":"In this paper we study conditions under which, for an inclusion of finite von Neumann algebras N ⊆ M , we have the reduced amalgamated free product * N M is embeddable into (R⊗N 1) ω for some other finite von Neumann algebra N 1 , where R is the hyperfinite II 1 factor.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius 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thumbnail of Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery" class="work-thumbnail" src="https://attachments.academia-assets.com/117036728/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354525/Entropy_Estimates_on_Tensor_Products_of_Banach_Spaces_and_Applications_to_Low_Rank_Recovery">Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery</a></div><div class="wp-workCard_item"><span>2019 13th International conference on Sampling Theory and Applications (SampTA)</span><span>, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Low-rank matrix models have been universally useful for numerous applications starting from class...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. The Schatten-1 norm, also known as the nuclear norm, has been used as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the Schatten-1 norm for low-rankness has a nice analogy with the 1 norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the Schatten-1 norm. Inspired by a recent work on the max-norm-based matrix completion, we provide a unified view on a class of tensor product norms and their interlacing relations on low-rank operators. Furthermore we derive entropy estimates between the injective and projective tensor products of a family of Banach space pairs and demonstrate their applications to matrix completion and decentralized subspace sketching.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="170ed7c832c50b2a5736a519e113f148" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036728,"asset_id":122354525,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036728/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354525"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354525"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354525; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354525]").text(description); $(".js-view-count[data-work-id=122354525]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354525; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354525']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354525, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "170ed7c832c50b2a5736a519e113f148" } } $('.js-work-strip[data-work-id=122354525]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354525,"title":"Entropy Estimates on Tensor Products of Banach Spaces and Applications to Low-Rank Recovery","translated_title":"","metadata":{"publisher":"IEEE","grobid_abstract":"Low-rank matrix models have been universally useful for numerous applications starting from classical system identification to more modern matrix completion in signal processing and statistics. 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Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\log^6(d_1 + d_2)/\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1b0f1fe5c42b7ab10612dcbcacdbb934" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036693,"asset_id":122354520,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354520"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354520"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354520; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354520]").text(description); $(".js-view-count[data-work-id=122354520]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354520; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354520']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354520, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1b0f1fe5c42b7ab10612dcbcacdbb934" } } $('.js-work-strip[data-work-id=122354520]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354520,"title":"Decentralized sketching of low rank matrices","translated_title":"","metadata":{"abstract":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","publisher":"NeurIPS","publication_date":{"day":null,"month":null,"year":2019,"errors":{}}},"translated_abstract":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","internal_url":"https://www.academia.edu/122354520/Decentralized_sketching_of_low_rank_matrices","translated_internal_url":"","created_at":"2024-07-25T22:49:32.304-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036693,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036693/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036693/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973178=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=YtbDygibkXF8d2TIEzHwYhtxhG8c-4B2bOdchva4ItFSEZa-jI~Bwwmj1kQ0NPmDAUTc4IDM77YoNRqxNilihx2HMSJFAMsKNvhMjMMz96eXlZL3u66E2rRwLIeg5z9YirZi5v9rFPzriSb75zPylledKv2bhEDiF164A~bVFstqidW7AJI5~pnFtaSz8Rc-~L1lK9IgOTxzoin4tSrWPutolrJGWDzX-tOtoSYErujlQC3YcR1wfVB4izWjaWtTB97gWtcDVnZ0OpiOPdL1B4oJmlNApjrJEWgdqG~Y0Y8SWpwtnmeaIXnWuH2FQORggtSodp1QUJcvlKOW-8Rjbg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Decentralized_sketching_of_low_rank_matrices","translated_slug":"","page_count":10,"language":"en","content_type":"Work","summary":"We address a low-rank matrix recovery problem where each column of a rank-r matrix X of size (d1,d2) is compressed beyond the point of recovery to size L with L \u0026lt;\u0026lt; d1. Leveraging the joint structure between the columns, we propose a method to recover the matrix to within an epsilon relative error in the Frobenius norm from a total of O(r(d_1 + d_2)\\log^6(d_1 + d_2)/\\epsilon^2) observations. This guarantee holds uniformly for all incoherent matrices of rank r. In our method, we propose to use a novel matrix norm called the mixed-norm along with the maximum l2 norm of the columns to design a novel convex relaxation for low-rank recovery that is tailored to our observation model. We also show that our proposed mixed-norm, the standard nuclear norm, and the max-norm are particular instances of convex regularization of low-rankness via tensor norms. Finally, we provide a scalable ADMM algorithm for the mixed-norm based method and demonstrate its empirical performance via large-scal...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117036693,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036693/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036693/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036693/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973178=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=YtbDygibkXF8d2TIEzHwYhtxhG8c-4B2bOdchva4ItFSEZa-jI~Bwwmj1kQ0NPmDAUTc4IDM77YoNRqxNilihx2HMSJFAMsKNvhMjMMz96eXlZL3u66E2rRwLIeg5z9YirZi5v9rFPzriSb75zPylledKv2bhEDiF164A~bVFstqidW7AJI5~pnFtaSz8Rc-~L1lK9IgOTxzoin4tSrWPutolrJGWDzX-tOtoSYErujlQC3YcR1wfVB4izWjaWtTB97gWtcDVnZ0OpiOPdL1B4oJmlNApjrJEWgdqG~Y0Y8SWpwtnmeaIXnWuH2FQORggtSodp1QUJcvlKOW-8Rjbg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":117036692,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036692/thumbnails/1.jpg","file_name":"9200-decentralized-sketching-of-low-rank-matrices.pdf","download_url":"https://www.academia.edu/attachments/117036692/download_file","bulk_download_file_name":"Decentralized_sketching_of_low_rank_matr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036692/9200-decentralized-sketching-of-low-rank-matrices-libre.pdf?1721973184=\u0026response-content-disposition=attachment%3B+filename%3DDecentralized_sketching_of_low_rank_matr.pdf\u0026Expires=1733905077\u0026Signature=fT8KhChf36HGXoFChcrpscXPN28s79xjtteQPQReNHbFKEos-y4I2XIUFPOuVsVYFN05JqXgMWZxq9UDRE7UHDipuiv0qQ2gIajTtk1kSSBmP~dVpKifcc-wVB8BYIG7GCNWh2wd2wHieaK4zUynB08iOMFXJBgeW~vQQBEtH~LuPvccK2KbK12eAuZgcYJdQYIWZ3WrCZ48QR6mOjYdGuVVFjSJMN0ItzyRJiZ1XKYTFtS3lv0ANh-jVGL~40hEncHUACXltxB9VE-~tlwFLcHqAE1sNtLD9K~NSEFmQqx0meYmDSkPPNG5mnu4DQYiUmJ8AHDZYTF0u8GIGzlP2w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":95988,"name":"Matrix Completion","url":"https://www.academia.edu/Documents/in/Matrix_Completion"},{"id":322514,"name":"Low-Rank Approximation","url":"https://www.academia.edu/Documents/in/Low-Rank_Approximation"},{"id":2720299,"name":"Matrix norm","url":"https://www.academia.edu/Documents/in/Matrix_norm"}],"urls":[{"id":43689352,"url":"http://papers.nips.cc/paper/9200-decentralized-sketching-of-low-rank-matrices.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122354517"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122354517/Capacity_Estimates_for_TRO_Channels"><img alt="Research paper thumbnail of Capacity Estimates for TRO Channels" class="work-thumbnail" src="https://attachments.academia-assets.com/117036687/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122354517/Capacity_Estimates_for_TRO_Channels">Capacity Estimates for TRO Channels</a></div><div class="wp-workCard_item"><span>arXiv: Quantum Physics</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Using the notion of TRO&#39;s (ternary ring of operators) and independence from operator algebra ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Using the notion of TRO&#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. This class goes beyond degradable channels. The estimate are based on a &quot;local comparison theorem&quot; for sandwiched R\&#39;enyi relative entropy and complex interpolation. As an application, we discover new small dimensional examples which admit an easy formula for quantum and private capacities.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="201c046d008ba2f272ae359a893531c6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117036687,"asset_id":122354517,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117036687/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122354517"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122354517"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122354517; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122354517]").text(description); $(".js-view-count[data-work-id=122354517]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122354517; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122354517']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122354517, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "201c046d008ba2f272ae359a893531c6" } } $('.js-work-strip[data-work-id=122354517]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122354517,"title":"Capacity Estimates for TRO Channels","translated_title":"","metadata":{"abstract":"Using the notion of TRO\u0026#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. 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As an application, we discover new small dimensional examples which admit an easy formula for quantum and private capacities.","internal_url":"https://www.academia.edu/122354517/Capacity_Estimates_for_TRO_Channels","translated_internal_url":"","created_at":"2024-07-25T22:49:31.731-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117036687,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117036687/thumbnails/1.jpg","file_name":"2017-01-20-Session-XA-Li-Gao.pdf","download_url":"https://www.academia.edu/attachments/117036687/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Capacity_Estimates_for_TRO_Channels.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117036687/2017-01-20-Session-XA-Li-Gao-libre.pdf?1721973186=\u0026response-content-disposition=attachment%3B+filename%3DCapacity_Estimates_for_TRO_Channels.pdf\u0026Expires=1733905077\u0026Signature=E1NJIp1TPXOA31482HEpLNhXYYTPpD0odYg0Luk05EcqhskCFwC2qgJYkyxYI4ttwLh12HI1PG4E5G2Nn8tD9Qeewu2EnIigGKpjyZD0VD9ye7wOiJFCr7vGx7WJKV1DUskGLduefT3wXYdS9K~gMN8nElQkH-up1D0PuE-hw98sUk2XPczUmYjFtxiYvs4RxSj9uC~I4~08ZfVOFlNC7IJfvOktPaH-G07fJ70lWQG-s6af9D4bc98X1YEij5Ba2uVYh6lpwDniWwLw57CXgGwIydTFPCxg2c~aZcd2lN899o-4AcwT87jekWz28dgPFXe7qN5DNkCM1Env54y36w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Capacity_Estimates_for_TRO_Channels","translated_slug":"","page_count":45,"language":"en","content_type":"Work","summary":"Using the notion of TRO\u0026#39;s (ternary ring of operators) and independence from operator algebra theory, we discover a new class of channels which allow single-letter bounds for their quantum and private capacity, as well as strong converse rates. This class goes beyond degradable channels. The estimate are based on a \u0026quot;local comparison theorem\u0026quot; for sandwiched R\\\u0026#39;enyi relative entropy and complex interpolation. 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Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase 'universal collective rotation channels' for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7e508a7694c6f6360c40eaefd01d1376" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034522,"asset_id":122351833,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351833"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351833"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351833; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351833]").text(description); $(".js-view-count[data-work-id=122351833]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351833; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351833']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351833, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "7e508a7694c6f6360c40eaefd01d1376" } } $('.js-work-strip[data-work-id=122351833]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351833,"title":"Quantum error correction and Young tableaux","translated_title":"","metadata":{"grobid_abstract":"A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase 'universal collective rotation channels' for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.","grobid_abstract_attachment_id":117034522},"translated_abstract":null,"internal_url":"https://www.academia.edu/122351833/Quantum_error_correction_and_Young_tableaux","translated_internal_url":"","created_at":"2024-07-25T19:01:19.892-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117034522,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034522/thumbnails/1.jpg","file_name":"0405032v2.pdf","download_url":"https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantum_error_correction_and_Young_table.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034522/0405032v2-libre.pdf?1721959986=\u0026response-content-disposition=attachment%3B+filename%3DQuantum_error_correction_and_Young_table.pdf\u0026Expires=1733905077\u0026Signature=CAiz7HcfywV6Bj8bSd1xn5HZPSMRqcJZgTh4oxJUdVlVCCBS~E57PMzCaz2W~5GmeH-3AsbWT5tVTxq5qaQByuhG6Es9TstKAU~EzBy8WyMd25zIdzeT1mOStGPjD~l1NkorZB7PGx-ed9TsEALi5MOqfhMmTQJCfMh2EAFze37h~knr8hqLnH1zMyTkOKNoS8fTm-sujc4v6uc0H452q7UunTNMjVPVNHqdKpW~ONRv0mOKNmBFESOLJyiqcmjfn6JFElzYKHfEixA4OX9JVPNjQbzltOffPaUY0Oyavnr4bdFBGs3-djhkXRVQiY8bQUPLmg~glk7CYZu-wpV-fA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Quantum_error_correction_and_Young_tableaux","translated_slug":"","page_count":25,"language":"en","content_type":"Work","summary":"A quantum channel is a completely positive trace preserving map which acts on the set of operators for the Hilbert space associated with a given quantum system. Analysis of such channels is central to quantum computing and quantum information theory. We present and investigate a new class of quantum channels that includes the class of collective rotation channels as a special case. We use the phrase 'universal collective rotation channels' for this class. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this operator algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We apply classical representation theory of the symmetric group via Young tableaux and give a computationally amenable method for explicitly finding this structure for the class of universal collective rotation channels.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117034522,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034522/thumbnails/1.jpg","file_name":"0405032v2.pdf","download_url":"https://www.academia.edu/attachments/117034522/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Quantum_error_correction_and_Young_table.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034522/0405032v2-libre.pdf?1721959986=\u0026response-content-disposition=attachment%3B+filename%3DQuantum_error_correction_and_Young_table.pdf\u0026Expires=1733905077\u0026Signature=CAiz7HcfywV6Bj8bSd1xn5HZPSMRqcJZgTh4oxJUdVlVCCBS~E57PMzCaz2W~5GmeH-3AsbWT5tVTxq5qaQByuhG6Es9TstKAU~EzBy8WyMd25zIdzeT1mOStGPjD~l1NkorZB7PGx-ed9TsEALi5MOqfhMmTQJCfMh2EAFze37h~knr8hqLnH1zMyTkOKNoS8fTm-sujc4v6uc0H452q7UunTNMjVPVNHqdKpW~ONRv0mOKNmBFESOLJyiqcmjfn6JFElzYKHfEixA4OX9JVPNjQbzltOffPaUY0Oyavnr4bdFBGs3-djhkXRVQiY8bQUPLmg~glk7CYZu-wpV-fA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122351832"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122351832/Operator_structures_in_quantum_information_theory"><img alt="Research paper thumbnail of Operator structures in quantum information theory" class="work-thumbnail" src="https://attachments.academia-assets.com/117034506/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122351832/Operator_structures_in_quantum_information_theory">Operator structures in quantum information theory</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Physicists have long recognized that the appropriate framework for quantum theory is that of a Hi...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B (H). This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗-algebras and W∗-algebras (with the latter also known as von Neumann algebras). In the 1970&#x27;s these were used extensively in the study of quantum statistical mechanics and quantum field theory. Although at the most basic level, quantum ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="95e909ca033ab8f0b68a8e17cb71f52c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034506,"asset_id":122351832,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034506/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351832"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351832"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351832; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351832]").text(description); $(".js-view-count[data-work-id=122351832]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351832; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351832']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351832, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "95e909ca033ab8f0b68a8e17cb71f52c" } } $('.js-work-strip[data-work-id=122351832]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351832,"title":"Operator structures in quantum information theory","translated_title":"","metadata":{"abstract":"Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B (H). This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗-algebras and W∗-algebras (with the latter also known as von Neumann algebras). In the 1970\u0026#x27;s these were used extensively in the study of quantum statistical mechanics and quantum field theory. Although at the most basic level, quantum ..."},"translated_abstract":"Physicists have long recognized that the appropriate framework for quantum theory is that of a Hilbert space H and in the simplest case the algebra of observables is contained in B (H). This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗-algebras and W∗-algebras (with the latter also known as von Neumann algebras). In the 1970\u0026#x27;s these were used extensively in the study of quantum statistical mechanics and quantum field theory. 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This motivated von Neumann to develop the more general framework of operator algebras and, in particular C∗-algebras and W∗-algebras (with the latter also known as von Neumann algebras). In the 1970\u0026#x27;s these were used extensively in the study of quantum statistical mechanics and quantum field theory. Although at the most basic level, quantum ...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117034506,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034506/thumbnails/1.jpg","file_name":"report12w5084.pdf","download_url":"https://www.academia.edu/attachments/117034506/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Operator_structures_in_quantum_informati.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034506/report12w5084-libre.pdf?1721959986=\u0026response-content-disposition=attachment%3B+filename%3DOperator_structures_in_quantum_informati.pdf\u0026Expires=1733905077\u0026Signature=bg~u5JdjZeYg5uOFw0NT9qdgJo74RpH6WK1V~Lxr2cbWEAEDYooxSIZ0rktXMTZGkS-17DB8TNO0udhGFZoEoAqiGvaO9LeroeFYKJH2-u~9Nrwl3V0w~Noml8ZfdIWRPtZl9X05LfuPwtOEdV8IcReO3PEBcNRHBgr-vf7~6o1~q39bcDu2ASaos8WtHFGpN1lh62CVttgRcyxxPODg0UhaxMqCYISI3mgGQp18qAXXCRzJe7QTkRplG33E0N45GNcdl6F6MmmAoIlHLDNILoYkroR7lTKUfNE-pckWcUCnQYo2mzPswa52AE7CZNGDyoG7FcXlb~M8z6NFieqO-g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":43687798,"url":"http://www.birs.ca/workshops/2012/12w5084/report12w5084.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="122351823"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/122351823/Stability_property_for_the_quantum_jump_operators_of_an_open_system"><img alt="Research paper thumbnail of Stability property for the quantum jump operators of an open system" class="work-thumbnail" src="https://attachments.academia-assets.com/117034502/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/122351823/Stability_property_for_the_quantum_jump_operators_of_an_open_system">Stability property for the quantum jump operators of an open system</a></div><div class="wp-workCard_item"><span>arXiv (Cornell University)</span><span>, Nov 14, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show the continuity property of spectral gaps and complete Logarithmic constants in terms of t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space and the technique developed in [18]. Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1a8178eb4dac98cc5920dbbb5b6f02bd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":117034502,"asset_id":122351823,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="122351823"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="122351823"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 122351823; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=122351823]").text(description); $(".js-view-count[data-work-id=122351823]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 122351823; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='122351823']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 122351823, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1a8178eb4dac98cc5920dbbb5b6f02bd" } } $('.js-work-strip[data-work-id=122351823]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":122351823,"title":"Stability property for the quantum jump operators of an open system","translated_title":"","metadata":{"publisher":"Cornell University","grobid_abstract":"We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space and the technique developed in [18]. Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.","publication_date":{"day":14,"month":11,"year":2022,"errors":{}},"publication_name":"arXiv (Cornell University)","grobid_abstract_attachment_id":117034502},"translated_abstract":null,"internal_url":"https://www.academia.edu/122351823/Stability_property_for_the_quantum_jump_operators_of_an_open_system","translated_internal_url":"","created_at":"2024-07-25T19:01:08.330-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":117034502,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034502/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034502/2211-libre.pdf?1721960002=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905077\u0026Signature=PlP1vZgB6cHH8w3QpDWwB5nmOaoZuT4KeTl5hdsxW4rhJ3CaTbX1CgpWyU~ImOceLiUNOU1OqjqMmWmUEZ6oPVNKih34KI3s5sIfVg3bRtRNWFd5OBPWlIgNCvoT13VISN1hWHYDTlNdfnljHQXoWR5Yf~~WfeMEqwdBFIstlT6qcAhN-R6-Q9GYx58A17kIvvvvWisawVxoBvIl1yVb9FXUxHnAW7KESu0L-kCTuezJ4YBXy1CNArSD86e7XRkwDdQ1w3OwwR3d0xOLm75BEmsWJMaHK~lqZfsN0pulxHsAfwWe3waahzntWTLO~mkzJ3LCeZp3BhXwO5CI6bRH8g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Stability_property_for_the_quantum_jump_operators_of_an_open_system","translated_slug":"","page_count":25,"language":"en","content_type":"Work","summary":"We show the continuity property of spectral gaps and complete Logarithmic constants in terms of the jump operators of Lindblad generators in finite dimensional setting. Our method is based on the bimodule structure of the derivation space and the technique developed in [18]. Using the same trick, we also show the continuity of the g 2 (0) constant used to distinguish quantum and classical lights in quantum optics.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":117034502,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034502/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034502/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034502/2211-libre.pdf?1721960002=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905077\u0026Signature=PlP1vZgB6cHH8w3QpDWwB5nmOaoZuT4KeTl5hdsxW4rhJ3CaTbX1CgpWyU~ImOceLiUNOU1OqjqMmWmUEZ6oPVNKih34KI3s5sIfVg3bRtRNWFd5OBPWlIgNCvoT13VISN1hWHYDTlNdfnljHQXoWR5Yf~~WfeMEqwdBFIstlT6qcAhN-R6-Q9GYx58A17kIvvvvWisawVxoBvIl1yVb9FXUxHnAW7KESu0L-kCTuezJ4YBXy1CNArSD86e7XRkwDdQ1w3OwwR3d0xOLm75BEmsWJMaHK~lqZfsN0pulxHsAfwWe3waahzntWTLO~mkzJ3LCeZp3BhXwO5CI6bRH8g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":117034501,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/117034501/thumbnails/1.jpg","file_name":"2211.pdf","download_url":"https://www.academia.edu/attachments/117034501/download_file","bulk_download_file_name":"Stability_property_for_the_quantum_jump.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/117034501/2211-libre.pdf?1721959997=\u0026response-content-disposition=attachment%3B+filename%3DStability_property_for_the_quantum_jump.pdf\u0026Expires=1733905078\u0026Signature=NgopP1jRsfVGjph1ETZM8W2Rrky0YUgBA289aC0u9X6hNiCbixlW9HYr5Q-CI1xLgdNI11ALZaLYNmVwi7FCXxgfoFU0G2ImPUsmJwe4ZYcgKTU9e9ZvMR5xcZ4DJ7BBy-uKq2h~gjjhUNkRly75y1tJ8MdcERUo7MPMlKsEcvxDgygMm3hTvMzKa8W4IRC0kEOf9~XJpsvxO2D1rC0Bc4lf24WiEhvzSn3zui3~2p3hF1-e65id49T1BRFMp5BVhlR9L9iQdyg5xMuMoXl8QItds-BZ~Z7Sb8o2Hnzblr1Gu1MGgKtaigd~smLbhiBFeAUcMyu5g7a7ouTOBec2Ww__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":14193,"name":"Philosophy of Property","url":"https://www.academia.edu/Documents/in/Philosophy_of_Property"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"},{"id":288502,"name":"Jump","url":"https://www.academia.edu/Documents/in/Jump"}],"urls":[{"id":43687790,"url":"http://arxiv.org/pdf/2211.07527"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776046"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program"><img alt="Research paper thumbnail of Approximately low-rank recovery from noisy and local measurements by convex program" class="work-thumbnail" src="https://attachments.academia-assets.com/112088105/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program">Approximately low-rank recovery from noisy and local measurements by convex program</a></div><div class="wp-workCard_item"><span>Information and Inference: A Journal of the IMA</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Low-rank matrix models have been universally useful for numerous applications, from classical sys...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="493993c26ad12229407e601af568438f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088105,"asset_id":115776046,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776046"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776046"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776046; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776046]").text(description); $(".js-view-count[data-work-id=115776046]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776046; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776046']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776046, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "493993c26ad12229407e601af568438f" } } $('.js-work-strip[data-work-id=115776046]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776046,"title":"Approximately low-rank recovery from noisy and local measurements by convex program","translated_title":"","metadata":{"abstract":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","publisher":"Oxford University Press (OUP)","publication_name":"Information and Inference: A Journal of the IMA"},"translated_abstract":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","internal_url":"https://www.academia.edu/115776046/Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program","translated_internal_url":"","created_at":"2024-03-04T07:00:29.007-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088105,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088105/thumbnails/1.jpg","file_name":"2110.15205v1.pdf","download_url":"https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Approximately_low_rank_recovery_from_noi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088105/2110.15205v1-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DApproximately_low_rank_recovery_from_noi.pdf\u0026Expires=1733905078\u0026Signature=AWUzdhhDHvcVd~i92PXc5I566P9EO8Rzryzrojqt-q5isz1nOuUGkZeDbbN6C8X4iy6OgKVPL3EcxP9kfLMV~ZRLPy9sWhJtXtV0A0Hau9yy5izeSbzMOPNpTNgcdY9ZhLDwojW9uG7k~DoEjqXQA1ApCQxc54A~UNifjo-9ai0KupRc5679RqqBeBZHS6lGFhvDGrY91C2x8rfzMvfmIOwS6D1Mi8l~JK1Bp1kkZcUy1HX~8P-987pvdDjMQd5KGl4hbqXN8Bgjh2tG1HgvBKVkHEP3KV6OKgxH2QrFiKUGOM~RB3Mnt09~ny6RPRCJyZvKu6k~5IJidqjwBP3LmA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Approximately_low_rank_recovery_from_noisy_and_local_measurements_by_convex_program","translated_slug":"","page_count":38,"language":"en","content_type":"Work","summary":"Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $\\ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088105,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088105/thumbnails/1.jpg","file_name":"2110.15205v1.pdf","download_url":"https://www.academia.edu/attachments/112088105/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Approximately_low_rank_recovery_from_noi.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088105/2110.15205v1-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DApproximately_low_rank_recovery_from_noi.pdf\u0026Expires=1733905078\u0026Signature=AWUzdhhDHvcVd~i92PXc5I566P9EO8Rzryzrojqt-q5isz1nOuUGkZeDbbN6C8X4iy6OgKVPL3EcxP9kfLMV~ZRLPy9sWhJtXtV0A0Hau9yy5izeSbzMOPNpTNgcdY9ZhLDwojW9uG7k~DoEjqXQA1ApCQxc54A~UNifjo-9ai0KupRc5679RqqBeBZHS6lGFhvDGrY91C2x8rfzMvfmIOwS6D1Mi8l~JK1Bp1kkZcUy1HX~8P-987pvdDjMQd5KGl4hbqXN8Bgjh2tG1HgvBKVkHEP3KV6OKgxH2QrFiKUGOM~RB3Mnt09~ny6RPRCJyZvKu6k~5IJidqjwBP3LmA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":85880,"name":"Singular value decomposition","url":"https://www.academia.edu/Documents/in/Singular_value_decomposition"},{"id":95988,"name":"Matrix Completion","url":"https://www.academia.edu/Documents/in/Matrix_Completion"},{"id":806332,"name":"Estimator","url":"https://www.academia.edu/Documents/in/Estimator"},{"id":2720299,"name":"Matrix norm","url":"https://www.academia.edu/Documents/in/Matrix_norm"},{"id":4113180,"name":"operator norm","url":"https://www.academia.edu/Documents/in/operator_norm"}],"urls":[{"id":40025902,"url":"https://academic.oup.com/imaiai/article-pdf/12/3/1612/51602778/iaad013.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776045"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings"><img alt="Research paper thumbnail of Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings" class="work-thumbnail" src="https://attachments.academia-assets.com/112088106/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings">Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Trace inequalities are general techniques with many applications in quantum information theory, o...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="160efed2c7e1239e4fa8538231832a94" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088106,"asset_id":115776045,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776045"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776045"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776045; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776045]").text(description); $(".js-view-count[data-work-id=115776045]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776045; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776045']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776045, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "160efed2c7e1239e4fa8538231832a94" } } $('.js-work-strip[data-work-id=115776045]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776045,"title":"Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings","translated_title":"","metadata":{"abstract":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","publisher":"AIP Publishing","publication_name":"Journal of Mathematical Physics"},"translated_abstract":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","internal_url":"https://www.academia.edu/115776045/Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings","translated_internal_url":"","created_at":"2024-03-04T07:00:28.767-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088106,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088106/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Multivariate_trace_inequalities_p_fideli.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088106/2009-libre.pdf?1709564797=\u0026response-content-disposition=attachment%3B+filename%3DMultivariate_trace_inequalities_p_fideli.pdf\u0026Expires=1733905078\u0026Signature=aAjkaPt27v9QIElemeJspBV6Vd00GAEXKMAUhJAV70VVwRzZ3orfZJwmhF7Q7RiQwrZN~3XWjl4v0r45xpF7YfesOaw3DGmoKya8lgaorblQ40vPvkcq7VdrMn~8flMzxnXXQZFPcfc2GOZVsKt92fnmm3uGuNUZHQ6DfkQCpOARfJ8PqJN~Lr8zOuG8eYsUgiohRAsXv~XDqRZ6oUzN8E2SQVx0~UfEcWfeI92hMzsNCFtDBVePjKAdhi8j3m87rYgjnT4wV0F-gCneLx9eMrbO4yVnPOIhcBIqrQphoz87f6YPgIaJE9andd2zrkloKE4bDxQTqV8inSnYMgCzkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Multivariate_trace_inequalities_p_fidelity_and_universal_recovery_beyond_tracial_settings","translated_slug":"","page_count":57,"language":"en","content_type":"Work","summary":"Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki–Lieb–Thirring and Golden–Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing t...","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088106,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088106/thumbnails/1.jpg","file_name":"2009.pdf","download_url":"https://www.academia.edu/attachments/112088106/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Multivariate_trace_inequalities_p_fideli.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088106/2009-libre.pdf?1709564797=\u0026response-content-disposition=attachment%3B+filename%3DMultivariate_trace_inequalities_p_fideli.pdf\u0026Expires=1733905078\u0026Signature=aAjkaPt27v9QIElemeJspBV6Vd00GAEXKMAUhJAV70VVwRzZ3orfZJwmhF7Q7RiQwrZN~3XWjl4v0r45xpF7YfesOaw3DGmoKya8lgaorblQ40vPvkcq7VdrMn~8flMzxnXXQZFPcfc2GOZVsKt92fnmm3uGuNUZHQ6DfkQCpOARfJ8PqJN~Lr8zOuG8eYsUgiohRAsXv~XDqRZ6oUzN8E2SQVx0~UfEcWfeI92hMzsNCFtDBVePjKAdhi8j3m87rYgjnT4wV0F-gCneLx9eMrbO4yVnPOIhcBIqrQphoz87f6YPgIaJE9andd2zrkloKE4bDxQTqV8inSnYMgCzkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":51108,"name":"Noncommutative Geometry","url":"https://www.academia.edu/Documents/in/Noncommutative_Geometry"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":403140,"name":"von Neumann algebra","url":"https://www.academia.edu/Documents/in/von_Neumann_algebra"},{"id":476286,"name":"Von Neumann Architecture","url":"https://www.academia.edu/Documents/in/Von_Neumann_Architecture"},{"id":2546925,"name":"von Neumann Entropy","url":"https://www.academia.edu/Documents/in/von_Neumann_Entropy"}],"urls":[{"id":40025901,"url":"https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0066653/16611663/122204_1_online.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776044"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure"><img alt="Research paper thumbnail of Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure" class="work-thumbnail" src="https://attachments.academia-assets.com/112088108/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure">Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure</a></div><div class="wp-workCard_item"><span>Journal of Statistical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroup...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint quantum Markov process can be used to prove estimates on the exponential convergence in relative entropy of quantum Markov systems which preserve a fixed state. This leads to estimates for the decay to equilibrium for coupled systems and to estimates for mixed state preparation times using Lindblad operators. Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1ebe2ac56fe2195348e371a73606793f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088108,"asset_id":115776044,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776044"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776044"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776044; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776044]").text(description); $(".js-view-count[data-work-id=115776044]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776044; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776044']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776044, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "1ebe2ac56fe2195348e371a73606793f" } } $('.js-work-strip[data-work-id=115776044]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776044,"title":"Stability of Logarithmic Sobolev Inequalities Under a Noncommutative Change of Measure","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. 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Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.","publication_name":"Journal of Statistical Physics","grobid_abstract_attachment_id":112088108},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776044/Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure","translated_internal_url":"","created_at":"2024-03-04T07:00:28.524-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088108,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088108/thumbnails/1.jpg","file_name":"1911.pdf","download_url":"https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_of_Logarithmic_Sobolev_Inequal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088108/1911-libre.pdf?1709564783=\u0026response-content-disposition=attachment%3B+filename%3DStability_of_Logarithmic_Sobolev_Inequal.pdf\u0026Expires=1733905078\u0026Signature=NLdru2Xzk4u31gDP8F9yeoSfq8Reu-FqPcp9q1GNCDQs~DMKi26UyVxHuOpiLj~r7wfQ4L5ntIt0Lp5itE~6yaHEESFKNJYCowmsakLb5dqK21tLQlWmwguBGC0P8g892X2FtkyAPBmTHfRfvs12HU-BeBdR5Dmfgjx3c5xNuhvvuPNq48-hJ9DJm5OSYodDiiGcsxy1lJWMLcSP-guLK0rUeH~qceZhamxd-qP9nYmbXBYMORqcGY4qgRNb-WZMod1ymgk-TDLLx~ECxBmYNdJc1hoq-AxCGBXy2rDLhzqQRjn-01hqYPm5cWCsy64g4rwnKx46TlA2b1Y2ZV8wVQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Stability_of_Logarithmic_Sobolev_Inequalities_Under_a_Noncommutative_Change_of_Measure","translated_slug":"","page_count":26,"language":"en","content_type":"Work","summary":"We generalize Holley-Stroock's perturbation argument from commutative to quantum Markov semigroups. As a consequence, results on (complete) modified logarithmic Sobolev inequalities and logarithmic Sobolev inequalities for self-adjoint quantum Markov process can be used to prove estimates on the exponential convergence in relative entropy of quantum Markov systems which preserve a fixed state. This leads to estimates for the decay to equilibrium for coupled systems and to estimates for mixed state preparation times using Lindblad operators. Our techniques also apply to discrete time settings, where we show that the strong data processing inequality constant of a quantum channel can be controlled by that of a corresponding unital channel.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088108,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088108/thumbnails/1.jpg","file_name":"1911.pdf","download_url":"https://www.academia.edu/attachments/112088108/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Stability_of_Logarithmic_Sobolev_Inequal.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088108/1911-libre.pdf?1709564783=\u0026response-content-disposition=attachment%3B+filename%3DStability_of_Logarithmic_Sobolev_Inequal.pdf\u0026Expires=1733905078\u0026Signature=NLdru2Xzk4u31gDP8F9yeoSfq8Reu-FqPcp9q1GNCDQs~DMKi26UyVxHuOpiLj~r7wfQ4L5ntIt0Lp5itE~6yaHEESFKNJYCowmsakLb5dqK21tLQlWmwguBGC0P8g892X2FtkyAPBmTHfRfvs12HU-BeBdR5Dmfgjx3c5xNuhvvuPNq48-hJ9DJm5OSYodDiiGcsxy1lJWMLcSP-guLK0rUeH~qceZhamxd-qP9nYmbXBYMORqcGY4qgRNb-WZMod1ymgk-TDLLx~ECxBmYNdJc1hoq-AxCGBXy2rDLhzqQRjn-01hqYPm5cWCsy64g4rwnKx46TlA2b1Y2ZV8wVQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":422,"name":"Computer Science","url":"https://www.academia.edu/Documents/in/Computer_Science"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":16460,"name":"Statistical Physics","url":"https://www.academia.edu/Documents/in/Statistical_Physics"},{"id":51108,"name":"Noncommutative Geometry","url":"https://www.academia.edu/Documents/in/Noncommutative_Geometry"},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":595993,"name":"Markov chain","url":"https://www.academia.edu/Documents/in/Markov_chain"},{"id":741671,"name":"Markov Process","url":"https://www.academia.edu/Documents/in/Markov_Process"},{"id":3193313,"name":"arXiv","url":"https://www.academia.edu/Documents/in/arXiv"},{"id":3292545,"name":"Logarithm","url":"https://www.academia.edu/Documents/in/Logarithm"}],"urls":[{"id":40025900,"url":"https://link.springer.com/content/pdf/10.1007/s10955-022-03026-x.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776043"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games"><img alt="Research paper thumbnail of On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games" class="work-thumbnail" src="https://attachments.academia-assets.com/112088099/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games">On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this work we show that, given a linear map from a general operator space into the dual of a C ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="31f2d837dc38193bea74f4439e19b3db" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088099,"asset_id":115776043,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776043"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776043"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776043; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776043]").text(description); $(".js-view-count[data-work-id=115776043]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776043; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776043']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776043, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "31f2d837dc38193bea74f4439e19b3db" } } $('.js-work-strip[data-work-id=115776043]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776043,"title":"On the relation between completely bounded and (1,cb)-summing maps with applications to quantum XOR games","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. 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In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.","publication_name":"Journal of Functional Analysis","grobid_abstract_attachment_id":112088099},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776043/On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games","translated_internal_url":"","created_at":"2024-03-04T07:00:28.276-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088099/thumbnails/1.jpg","file_name":"2112.05214v1.pdf","download_url":"https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_the_relation_between_completely_bound.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088099/2112.05214v1-libre.pdf?1709564781=\u0026response-content-disposition=attachment%3B+filename%3DOn_the_relation_between_completely_bound.pdf\u0026Expires=1733905078\u0026Signature=RQzLzcve4AWr8l8UmD5UOG97-ekR0B1wXlbGolNF1r~Bh8t8VGRHTSU43rSabCz9zXKFFFvLUL4lZubQ4ZQGHcQ5rGFeNA4ruF3W6Mt5GrMgFD3ftqmMR2ruQ7PpC-NLo~60HKl5UGY9S5-PPBz21QuKAlzMPVz3mGkpLHITVMbgQ6eJBGvFUcCTupAIp-C7BtKgkafPGTu7IY9427WaH6wSb0oydM1MRwG5fJLM7ALGIQf263BMTM0B4BQkiOqUTTJlik2J~Lz~TYsSC1PJNbe2uBc-bHilnN~k1b7mNZmJwqzv0UtnC8xrcTIfpXbCpDbS5b3y~LRE~x1L5LKhTA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_the_relation_between_completely_bounded_and_1_cb_summing_maps_with_applications_to_quantum_XOR_games","translated_slug":"","page_count":23,"language":"en","content_type":"Work","summary":"In this work we show that, given a linear map from a general operator space into the dual of a C *-algebra, its completely bounded norm is upper bounded by a universal constant times its (1, cb)-summing norm. This problem is motivated by the study of quantum XOR games in the field of quantum information theory. In particular, our results imply that for such games entangled strategies cannot be arbitrarily better than those strategies using one-way classical communication.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088099/thumbnails/1.jpg","file_name":"2112.05214v1.pdf","download_url":"https://www.academia.edu/attachments/112088099/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_the_relation_between_completely_bound.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088099/2112.05214v1-libre.pdf?1709564781=\u0026response-content-disposition=attachment%3B+filename%3DOn_the_relation_between_completely_bound.pdf\u0026Expires=1733905078\u0026Signature=RQzLzcve4AWr8l8UmD5UOG97-ekR0B1wXlbGolNF1r~Bh8t8VGRHTSU43rSabCz9zXKFFFvLUL4lZubQ4ZQGHcQ5rGFeNA4ruF3W6Mt5GrMgFD3ftqmMR2ruQ7PpC-NLo~60HKl5UGY9S5-PPBz21QuKAlzMPVz3mGkpLHITVMbgQ6eJBGvFUcCTupAIp-C7BtKgkafPGTu7IY9427WaH6wSb0oydM1MRwG5fJLM7ALGIQf263BMTM0B4BQkiOqUTTJlik2J~Lz~TYsSC1PJNbe2uBc-bHilnN~k1b7mNZmJwqzv0UtnC8xrcTIfpXbCpDbS5b3y~LRE~x1L5LKhTA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":69262,"name":"Quantum","url":"https://www.academia.edu/Documents/in/Quantum"}],"urls":[{"id":40025899,"url":"https://api.elsevier.com/content/article/PII:S0022123622003287?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776042"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel"><img alt="Research paper thumbnail of The Communication Value of a Quantum Channel" class="work-thumbnail" src="https://attachments.academia-assets.com/112088098/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel">The Communication Value of a Quantum Channel</a></div><div class="wp-workCard_item"><span>2022 IEEE International Symposium on Information Theory (ISIT)</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">There are various ways to quantify the communication capabilities of a quantum channel. In this w...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4c34c78d284e4b2257b7f87b239cf598" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088098,"asset_id":115776042,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776042"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776042"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776042; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776042]").text(description); $(".js-view-count[data-work-id=115776042]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776042; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776042']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776042, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4c34c78d284e4b2257b7f87b239cf598" } } $('.js-work-strip[data-work-id=115776042]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776042,"title":"The Communication Value of a Quantum Channel","translated_title":"","metadata":{"publisher":"IEEE","grobid_abstract":"There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.","publication_name":"2022 IEEE International Symposium on Information Theory (ISIT)","grobid_abstract_attachment_id":112088098},"translated_abstract":null,"internal_url":"https://www.academia.edu/115776042/The_Communication_Value_of_a_Quantum_Channel","translated_internal_url":"","created_at":"2024-03-04T07:00:28.022-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088098/thumbnails/1.jpg","file_name":"2109.11144v1.pdf","download_url":"https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_Communication_Value_of_a_Quantum_Cha.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088098/2109.11144v1-libre.pdf?1709564793=\u0026response-content-disposition=attachment%3B+filename%3DThe_Communication_Value_of_a_Quantum_Cha.pdf\u0026Expires=1733905078\u0026Signature=Bs59dhxY2XO5ErQlF8Ng8juDBF5Vg9-C1XdKgJ7YgAuXjDEeVmDNEEKMOsNO7c6uqhF5UGd~ujzRpyDoVm1qsbnVCoHym00FL5Am6f3BIlxJksuWYnqgMXmcqKG5dCs3vaD5OoRRVbmTg-Y8zCU9RV-jQoT1eHrqUVuWc4unUsJB~egEmIUphlCxcJyn4Q5h-nJ5ZhRftuLoR2Hp9uaoWf-TpHqrQfK3Lbyy~JJBlb7BkD~E1xNG4UUZHUXuHV47Vw0KfdqNEpILY-wRXziGkwL3-aNp4qpADmlq7wCInop4Jih6r-F-XhB6j8d6CMBP825zqB-sRK2BDwtkzwC2Sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"The_Communication_Value_of_a_Quantum_Channel","translated_slug":"","page_count":21,"language":"en","content_type":"Work","summary":"There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088098/thumbnails/1.jpg","file_name":"2109.11144v1.pdf","download_url":"https://www.academia.edu/attachments/112088098/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"The_Communication_Value_of_a_Quantum_Cha.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088098/2109.11144v1-libre.pdf?1709564793=\u0026response-content-disposition=attachment%3B+filename%3DThe_Communication_Value_of_a_Quantum_Cha.pdf\u0026Expires=1733905078\u0026Signature=Bs59dhxY2XO5ErQlF8Ng8juDBF5Vg9-C1XdKgJ7YgAuXjDEeVmDNEEKMOsNO7c6uqhF5UGd~ujzRpyDoVm1qsbnVCoHym00FL5Am6f3BIlxJksuWYnqgMXmcqKG5dCs3vaD5OoRRVbmTg-Y8zCU9RV-jQoT1eHrqUVuWc4unUsJB~egEmIUphlCxcJyn4Q5h-nJ5ZhRftuLoR2Hp9uaoWf-TpHqrQfK3Lbyy~JJBlb7BkD~E1xNG4UUZHUXuHV47Vw0KfdqNEpILY-wRXziGkwL3-aNp4qpADmlq7wCInop4Jih6r-F-XhB6j8d6CMBP825zqB-sRK2BDwtkzwC2Sw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":43591,"name":"Quantum entanglement","url":"https://www.academia.edu/Documents/in/Quantum_entanglement"},{"id":4027512,"name":"Quantum Channel","url":"https://www.academia.edu/Documents/in/Quantum_Channel"}],"urls":[{"id":40025898,"url":"http://xplorestaging.ieee.org/ielx7/9834325/9834269/09834380.pdf?arnumber=9834380"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776041"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776041/q_Chaos"><img alt="Research paper thumbnail of q-Chaos" class="work-thumbnail" src="https://attachments.academia-assets.com/112088025/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776041/q_Chaos">q-Chaos</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1)...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1&lt;q&lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d11989a6ee53becec35f85a5efbcf3e7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088025,"asset_id":115776041,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776041"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776041"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776041; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776041]").text(description); $(".js-view-count[data-work-id=115776041]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776041; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776041']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776041, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d11989a6ee53becec35f85a5efbcf3e7" } } $('.js-work-strip[data-work-id=115776041]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776041,"title":"q-Chaos","translated_title":"","metadata":{"abstract":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","publication_date":{"day":24,"month":1,"year":2008,"errors":{}}},"translated_abstract":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","internal_url":"https://www.academia.edu/115776041/q_Chaos","translated_internal_url":"","created_at":"2024-03-04T07:00:27.792-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088025,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088025/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088025/0801.3704v1-libre.pdf?1709564790=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=aSPHr4ylsRcdO0VXxunjwgE1mpMWAvJhC0TEuchL7lgnQRXsmCuodMw~dY-yMQt0cGFUJwkBX~2N6H~~y-EiI4a5PjKcq9G5kBS9SGl1vVTuiW1h0CVesBwc89SxZ2MDnEyj7bezfMtW8EYfxxjRP12~T0fBON9GSoCnjQVIA~etLatdC3HFJmEhN4JCBmRdcLXr0SsR6-SEC7Dw1VSgZxhIZp0js~yUqDOWp7nfWw6hiuM844wKBYoul4h9WlRMKTOrBBz1zOfZ65uMUAdHQjTlLI3~3o3OaIQmTAxahAeQT7uGNNxC~IIKmymwmSz-5nmsuhX5-zKIcyjaPOmOkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"q_Chaos","translated_slug":"","page_count":22,"language":"en","content_type":"Work","summary":"We consider the L_p norm estimates for homogeneous polynomials of q-gaussian variables (-1≤ q≤ 1). When -1\u0026lt;q\u0026lt;1 the L_p estimates for 1≤ p ≤ 2 are essentially the same as the free case (q=0), whilst the L_p estimates for 2≤ p ≤∞ show a strong q-dependence. Moreover, the extremal cases q = ± 1 produce decisively different formulae.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088025,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088025/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088025/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088025/0801.3704v1-libre.pdf?1709564790=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=aSPHr4ylsRcdO0VXxunjwgE1mpMWAvJhC0TEuchL7lgnQRXsmCuodMw~dY-yMQt0cGFUJwkBX~2N6H~~y-EiI4a5PjKcq9G5kBS9SGl1vVTuiW1h0CVesBwc89SxZ2MDnEyj7bezfMtW8EYfxxjRP12~T0fBON9GSoCnjQVIA~etLatdC3HFJmEhN4JCBmRdcLXr0SsR6-SEC7Dw1VSgZxhIZp0js~yUqDOWp7nfWw6hiuM844wKBYoul4h9WlRMKTOrBBz1zOfZ65uMUAdHQjTlLI3~3o3OaIQmTAxahAeQT7uGNNxC~IIKmymwmSz-5nmsuhX5-zKIcyjaPOmOkg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088024,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088024/thumbnails/1.jpg","file_name":"0801.3704v1.pdf","download_url":"https://www.academia.edu/attachments/112088024/download_file","bulk_download_file_name":"q_Chaos.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088024/0801.3704v1-libre.pdf?1709564780=\u0026response-content-disposition=attachment%3B+filename%3Dq_Chaos.pdf\u0026Expires=1733905078\u0026Signature=NOmyxr-S86jVkXCDcnddcpfdrpQ4Es9RTSQ3nlnQCS4USVphJzkgtJFnpklxGFn5tHHctU8HqJoixTaxbTqQoxJMpAsQK-bbESc9nZYjOhr6afYeuOgINdjGMu-rFqZQX-gzEEZOrl7CLvDTyUvGO49fRbXi64dr-M7lah8-zRcCK0oT5rQScpuqTiv4GZvXVgXnPmDAIKMzKD2yL54TJ9FJMFvZfkm2wZ7KMtFK0C8NHIrH9rLKoQN1xeZb1~3ZNqAplNSmzBtiIN4xqAF6jDAuFDFBloriA8P4yC7LBy~RsrrsOa0u2dPx81dDevR6DmTbrZkPxCk7kdDnxjjNGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":40025897,"url":"https://arxiv.org/pdf/0801.3704v1.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776040"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776040/Associated_with_Semigroups"><img alt="Research paper thumbnail of Associated with Semigroups" class="work-thumbnail" src="https://attachments.academia-assets.com/112088023/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776040/Associated_with_Semigroups">Associated with Semigroups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This article is an introduction to our recent work in harmonic analysis associated with semigroup...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calderón-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics-or with very little information on the metric-Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting but it is also valid in classical/commutative frameworks.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fda1e07e6dbf76ec5cefe54fcd7bf1a4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088023,"asset_id":115776040,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088023/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776040"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776040"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776040; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776040]").text(description); $(".js-view-count[data-work-id=115776040]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776040; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776040']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776040, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "fda1e07e6dbf76ec5cefe54fcd7bf1a4" } } $('.js-work-strip[data-work-id=115776040]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776040,"title":"Associated with Semigroups","translated_title":"","metadata":{"grobid_abstract":"This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calderón-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics-or with very little information on the metric-Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. 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Then, the following equivalence of norms holds whenever 1 ≤ q ≤ p &lt; ∞ (Σpq)</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b6950e0f9eb4f98e6f53d448fa1c472d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088093,"asset_id":115776037,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088093/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776037"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776037"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776037; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776037]").text(description); $(".js-view-count[data-work-id=115776037]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776037; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776037']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776037, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "b6950e0f9eb4f98e6f53d448fa1c472d" } } $('.js-work-strip[data-work-id=115776037]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776037,"title":"Theory of Amalgamated","translated_title":"","metadata":{"abstract":"Let f1, f2,..., fn be a family of independent copies of a given random variable f in a probability space (Ω, F, µ). 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Then, the following equivalence of norms holds whenever 1 ≤ q ≤ p \u0026lt; ∞ (Σpq)","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088093/thumbnails/1.jpg","file_name":"0511406v2.pdf","download_url":"https://www.academia.edu/attachments/112088093/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Theory_of_Amalgamated.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088093/0511406v2-libre.pdf?1709564891=\u0026response-content-disposition=attachment%3B+filename%3DTheory_of_Amalgamated.pdf\u0026Expires=1733905078\u0026Signature=GG0nnPyy6SVUNMD903oMyqQXVt3~AaJ-bfxi6XfpQY9xneEruBXWSuMlMUm77OP-PAfcLSVcbYtmw2FgDvyLRywOTBW50sJka~0hnsS0Eq8fQsTyz6Tmrt77t7ZpaDJAXpUfP9uuz3~CRxKFGG6WROA4GHptZfBWTvWTmPEG0hEBYlzi-Vrou4sz~c1-uMf~RQrRPmswC9cheeFr169WXYlP1q2Q~oamlSDTdGoEQIBtDPkFwgn4Akhm64PPpDMTjSLA3FXavycUDe9KTYmztQNdOhp7d2H-lxXjxfwnNDj0LZ4Cx~QnSKyXsF2xcptGLGgbxJaCjFUxNaEl8EsrNg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[{"id":40025894,"url":"http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.241.3266\u0026rep=rep1\u0026type=pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776036"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras"><img alt="Research paper thumbnail of Ultraproduct methods for mixed $q$-Gaussian algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112088020/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras">Ultraproduct methods for mixed $q$-Gaussian algebras</a></div><div class="wp-workCard_item"><span>arXiv: Operator Algebras</span><span>, 2015</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian alge...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\delta_{ij}$. Here we also allow equality in $-1\le q_{ij}=q_{ji}\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher&#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\&#39;e inequalities with constants $C\sqrt{p}$.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e5b14f8ea4427f83a4c293c1ea5cdfa0" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088020,"asset_id":115776036,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776036"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776036"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776036; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776036]").text(description); $(".js-view-count[data-work-id=115776036]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776036; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776036']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776036, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e5b14f8ea4427f83a4c293c1ea5cdfa0" } } $('.js-work-strip[data-work-id=115776036]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776036,"title":"Ultraproduct methods for mixed $q$-Gaussian algebras","translated_title":"","metadata":{"abstract":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","ai_title_tag":"Unified Ultraproduct Approach for Mixed q-Gaussian Algebras","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"arXiv: Operator Algebras"},"translated_abstract":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","internal_url":"https://www.academia.edu/115776036/Ultraproduct_methods_for_mixed_q_Gaussian_algebras","translated_internal_url":"","created_at":"2024-03-04T07:00:26.374-08:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":146358351,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112088020,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088020/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088020/1505.07852v2-libre.pdf?1709564801=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=XGM3HZ9iGbbV-q5Ph~~FVQfwj09~w2whbaGIf8whJwy1yZAOy5Mm690xY4MsA3gcaSDnVVBbQ~Kt~L4ZbREXvCCIM0J7d5w1C2NgmQr0CBWIbMvbn2QSiGNj4ftkQvnZOkEc8JzPf-yLRlMq91JleG1ySiAbKsSUZtq86Mz8D-2zf5xoValm6yUImKZn4hH~e1t0j-VeYhQXzL-1I8f1QfemwLXdfkbd1fWydKw9TzSwK8xAraNEAtYrcl028-aI97ai0yFXGO94Sd4sAgyZ-FaX~VXw--AzOyhe6shNcgg5Po-6JRRCk~AqCQf1rdkMxAFpCIbIuaCq9XR3uaGSxg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Ultraproduct_methods_for_mixed_q_Gaussian_algebras","translated_slug":"","page_count":47,"language":"en","content_type":"Work","summary":"We provide a unified ultraproduct approach for constructing Wick words in mixed $q$-Gaussian algebras, which are generated by $s_j=a_j+a_j^*$, $j=1,\\cdots,N$, where $a_ia^*_j - q_{ij}a^*_ja_i =\\delta_{ij}$. Here we also allow equality in $-1\\le q_{ij}=q_{ji}\\le 1$. Using the ultraproduct method, we construct an approximate co-multiplication of the mixed $q$-Gaussian algebras. Based on this we prove that these algebras are weakly amenable and strongly solid in the sense of Ozawa and Popa. We also encode Speicher\u0026#39;s central limit theorem in the unified ultraproduct method, and show that the Ornstein--Uhlenbeck semigroup is hypercontractive, the Riesz transform associated to the number operator is bounded, and the number operator satisfies the $L_p$ Poincar\\\u0026#39;e inequalities with constants $C\\sqrt{p}$.","owner":{"id":146358351,"first_name":"Marius","middle_initials":null,"last_name":"Junge","page_name":"JungeM","domain_name":"independent","created_at":"2020-02-18T14:04:29.113-08:00","display_name":"Marius Junge","url":"https://independent.academia.edu/JungeM"},"attachments":[{"id":112088020,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088020/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088020/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088020/1505.07852v2-libre.pdf?1709564801=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=XGM3HZ9iGbbV-q5Ph~~FVQfwj09~w2whbaGIf8whJwy1yZAOy5Mm690xY4MsA3gcaSDnVVBbQ~Kt~L4ZbREXvCCIM0J7d5w1C2NgmQr0CBWIbMvbn2QSiGNj4ftkQvnZOkEc8JzPf-yLRlMq91JleG1ySiAbKsSUZtq86Mz8D-2zf5xoValm6yUImKZn4hH~e1t0j-VeYhQXzL-1I8f1QfemwLXdfkbd1fWydKw9TzSwK8xAraNEAtYrcl028-aI97ai0yFXGO94Sd4sAgyZ-FaX~VXw--AzOyhe6shNcgg5Po-6JRRCk~AqCQf1rdkMxAFpCIbIuaCq9XR3uaGSxg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112088021,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112088021/thumbnails/1.jpg","file_name":"1505.07852v2.pdf","download_url":"https://www.academia.edu/attachments/112088021/download_file","bulk_download_file_name":"Ultraproduct_methods_for_mixed_q_Gaussia.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112088021/1505.07852v2-libre.pdf?1709564802=\u0026response-content-disposition=attachment%3B+filename%3DUltraproduct_methods_for_mixed_q_Gaussia.pdf\u0026Expires=1733905078\u0026Signature=ZKIGhZ9nFaJsjepIbvxDQe7q8~Quv4BOQsRYOu9Ii2VVDaUxhmODs0Iway1JMQuqfZLrEZ1p8BOv~wSnmu7PZK4UOO~-snxegILphpHyxx3Tyz~L44iuFCBtd9VrhAbrBXhXXB34lqhiSLRjTe4HkJB6VvBcy7fF8MwWEAl76CaltPbLobL54XWP2bJL05rCOqz07g-J1sKMv2U7e21nsiW51p6Lo-9rc0oXs9UYQI4J4UYKX-ymBqoJwxZ56uyjZYBjfhH-u0TaJKdohjk-Z5zS4tlnLx-9voKyhs2OV7OuUqmbs4OGlZOsEQ9sHxl67CBq68Pb3WwTBZDxcBVRkA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics"},{"id":342314,"name":"Gaussian","url":"https://www.academia.edu/Documents/in/Gaussian"},{"id":498860,"name":"Semigroup","url":"https://www.academia.edu/Documents/in/Semigroup"}],"urls":[{"id":40025893,"url":"https://arxiv.org/pdf/1505.07852v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115776035"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115776035/Universal_recovery_and_p_fidelity_in_von_Neumann_algebras"><img alt="Research paper thumbnail of Universal recovery and p-fidelity in von Neumann algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112088018/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115776035/Universal_recovery_and_p_fidelity_in_von_Neumann_algebras">Universal recovery and p-fidelity in von Neumann algebras</a></div><div class="wp-workCard_item"><span>arXiv: Quantum Physics</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Scenarios ranging from quantum error correction to high energy physics use recovery maps, which t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. The decrease in quantum relative entropy between two states under the same channel quantifies information lost. A small decrease in relative entropy often implies recoverability via a universal map depending only the second argument to the relative entropy. We find such a universal recovery map for arbitrary channels on von Neumann algebras, and we generalize to p-fidelity via subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that non-decrease of relative entropy is equivalent to the existence of an L 1 -isometry implementing the channel on both input states. Our primary technique is a reduction method by Haagerup, approximating a non-tracial, type III von Neumann algebra by a finite algebra. This technique has many potential applications in porting results from quantum information theory to...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="3775c8a2cfc9821643cf25060141286f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112088018,"asset_id":115776035,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112088018/download_file?st=MTczMzkwNDM2OCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115776035"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115776035"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115776035; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=115776035]").text(description); $(".js-view-count[data-work-id=115776035]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 115776035; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='115776035']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 115776035, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "3775c8a2cfc9821643cf25060141286f" } } $('.js-work-strip[data-work-id=115776035]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":115776035,"title":"Universal recovery and p-fidelity in von Neumann algebras","translated_title":"","metadata":{"abstract":"Scenarios ranging from quantum error correction to high energy physics use recovery maps, which try to reverse the effects of generally irreversible quantum channels. 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