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<div class="control is-expanded"> <label for="query" class="hidden-label">Search term or terms</label> <input class="input is-medium" id="query" name="query" placeholder="Search term..." type="text" value="Pu, Y -"> </div> <div class="select control is-medium"> <label class="is-hidden" for="searchtype">Field</label> <select class="is-medium" id="searchtype" name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author 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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Pu, Y -"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" 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is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2405.13369">arXiv:2405.13369</a> <span> [<a href="https://arxiv.org/pdf/2405.13369">pdf</a>, <a href="https://arxiv.org/format/2405.13369">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Realization of a crosstalk-free multi-ion node for long-distance quantum networking </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Lai%2C+P+-">P. -C. Lai</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Shi%2C+J+-">J. -X. Shi</a>, <a href="/search/quant-ph?searchtype=author&query=Cui%2C+Z+-">Z. -B. Cui</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Z+-">Z. -Q. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+S">S. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Liu%2C+P+-">P. -Y. Liu</a>, <a href="/search/quant-ph?searchtype=author&query=Tian%2C+Z+-">Z. -C. Tian</a>, <a href="/search/quant-ph?searchtype=author&query=Sun%2C+Y+-">Y. -D. Sun</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+X+-">X. -Y. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -Y. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Xu%2C+Y">Y. Xu</a>, <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2405.13369v1-abstract-short" style="display: inline;"> Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish entangling interface with telecom photons; and the other type, called the memory qubit, to… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13369v1-abstract-full').style.display = 'inline'; document.getElementById('2405.13369v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2405.13369v1-abstract-full" style="display: none;"> Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish entangling interface with telecom photons; and the other type, called the memory qubit, to store quantum information immune from photon scattering under entangling attempts. Here, we report the first experimental implementation of a telecom-compatible and crosstalk-free quantum network node based on two trapped $^{40}$Ca$^{+}$ ions. The memory qubit is encoded on a long-lived metastable level to avoid crosstalk with the communication qubit encoded in another subspace of the same ion species, and a quantum wavelength conversion module is employed to generate ion-photon entanglement over a $12\,$km fiber in a heralded style. Our work therefore constitutes an important step towards the realization of quantum repeaters and long-distance quantum networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2405.13369v1-abstract-full').style.display = 'none'; document.getElementById('2405.13369v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 12 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.14405">arXiv:2306.14405</a> <span> [<a href="https://arxiv.org/pdf/2306.14405">pdf</a>, <a href="https://arxiv.org/format/2306.14405">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Realization of a crosstalk-avoided quantum network node with dual-type qubits by the same ion species </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Feng%2C+L">L. Feng</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+Y+-">Y. -Y Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Guo%2C+W+-">W. -X. Guo</a>, <a href="/search/quant-ph?searchtype=author&query=Ma%2C+J+-">J. -Y. Ma</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+H+-">H. -X. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+L">L. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Wang%2C+Y">Y. Wang</a>, <a href="/search/quant-ph?searchtype=author&query=Huang%2C+C+-">C. -X. Huang</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+C">C. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Yao%2C+L">L. Yao</a>, <a href="/search/quant-ph?searchtype=author&query=Qi%2C+B+-">B. -X. Qi</a>, <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Zhou%2C+Z+-">Z. -C. Zhou</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.14405v2-abstract-short" style="display: inline;"> Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the porti… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14405v2-abstract-full').style.display = 'inline'; document.getElementById('2306.14405v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.14405v2-abstract-full" style="display: none;"> Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the portion and the location of different ion species, and can be subject to inefficient sympathetic cooling. Here we demonstrate a trapped-ion quantum network node in the dual-type qubit scheme where two types of qubits are encoded in the $S$ and $F$ hyperfine structure levels of ${}^{171}\mathrm{Yb}^+$ ions. We generate ion photon entanglement for the $S$-qubit in a typical timescale of hundreds of milliseconds, and verify its small crosstalk on a nearby $F$-qubit with coherence time above seconds. Our work demonstrates an enabling function of the dual-type qubit scheme for scalable quantum networks. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14405v2-abstract-full').style.display = 'none'; document.getElementById('2306.14405v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.09643">arXiv:1904.09643</a> <span> [<a href="https://arxiv.org/pdf/1904.09643">pdf</a>, <a href="https://arxiv.org/format/1904.09643">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/s41534-019-0144-0">10.1038/s41534-019-0144-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Experimental realization of 105-qubit random access quantum memory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+N">N. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+W">W. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+C">C. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+S">S. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.09643v2-abstract-short" style="display: inline;"> Random access memory is an indispensable device for classical information technology. Analog to this, for quantum information technology, it is desirable to have a random access quantum memory with many memory cells and programmable access to each cell. We report an experiment that realizes a random access quantum memory of 105 qubits carried by 210 memory cells in a macroscopic atomic ensemble. W… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.09643v2-abstract-full').style.display = 'inline'; document.getElementById('1904.09643v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.09643v2-abstract-full" style="display: none;"> Random access memory is an indispensable device for classical information technology. Analog to this, for quantum information technology, it is desirable to have a random access quantum memory with many memory cells and programmable access to each cell. We report an experiment that realizes a random access quantum memory of 105 qubits carried by 210 memory cells in a macroscopic atomic ensemble. We demonstrate storage of optical qubits into these memory cells and their read-out at programmable times by arbitrary orders with fidelities exceeding any classical bound. Experimental realization of a random access quantum memory with many memory cells and programmable control of its write-in and read-out makes an important step for its application in quantum communication, networking, and computation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.09643v2-abstract-full').style.display = 'none'; document.getElementById('1904.09643v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> npj Quantum Information 5, 28 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.09701">arXiv:1707.09701</a> <span> [<a href="https://arxiv.org/pdf/1707.09701">pdf</a>, <a href="https://arxiv.org/format/1707.09701">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1126/sciadv.aar3931">10.1126/sciadv.aar3931 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Experimental entanglement of 25 individually accessible atomic quantum interfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Wu%2C+Y+-">Y. -K. Wu</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+N">N. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+W">W. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+C">C. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Zhang%2C+S">S. Zhang</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.09701v2-abstract-short" style="display: inline;"> Quantum interface links stationary qubits in quantum memory with flying photonic qubits in optical transmission channels and constitutes a critical element for future quantum internet. Entanglement of quantum interfaces is a key step for realization of quantum networks. Through heralded detection of photon interference, here we generate multipartite entanglement between 25 (or 9) individually addr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.09701v2-abstract-full').style.display = 'inline'; document.getElementById('1707.09701v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.09701v2-abstract-full" style="display: none;"> Quantum interface links stationary qubits in quantum memory with flying photonic qubits in optical transmission channels and constitutes a critical element for future quantum internet. Entanglement of quantum interfaces is a key step for realization of quantum networks. Through heralded detection of photon interference, here we generate multipartite entanglement between 25 (or 9) individually addressable quantum interfaces in a multiplexed atomic quantum memory array and confirm genuine 22 (or 9) partite entanglement, respectively. Experimental entanglement of a record-high number of quantum interfaces makes an important enabling step towards realization of quantum networks, long-distance quantum communication, and multipartite quantum information processing. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.09701v2-abstract-full').style.display = 'none'; document.getElementById('1707.09701v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Sci. Adv. 4, eaar3931 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.07267">arXiv:1707.07267</a> <span> [<a href="https://arxiv.org/pdf/1707.07267">pdf</a>, <a href="https://arxiv.org/format/1707.07267">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1038/ncomms15359">10.1038/ncomms15359 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Experimental realization of a multiplexed quantum memory with 225 individually accessible memory cells </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/quant-ph?searchtype=author&query=Pu%2C+Y+-">Y. -F. Pu</a>, <a href="/search/quant-ph?searchtype=author&query=Jiang%2C+N">N. Jiang</a>, <a href="/search/quant-ph?searchtype=author&query=Chang%2C+W">W. Chang</a>, <a href="/search/quant-ph?searchtype=author&query=Yang%2C+H+-">H. -X. Yang</a>, <a href="/search/quant-ph?searchtype=author&query=Li%2C+C">C. Li</a>, <a href="/search/quant-ph?searchtype=author&query=Duan%2C+L+-">L. -M. Duan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.07267v1-abstract-short" style="display: inline;"> To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key ele… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.07267v1-abstract-full').style.display = 'inline'; document.getElementById('1707.07267v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.07267v1-abstract-full" style="display: none;"> To realize long-distance quantum communication and quantum network, it is required to have multiplexed quantum memory with many memory cells. Each memory cell needs to be individually addressable and independently accessible. Here we report an experiment that realizes a multiplexed DLCZ-type quantum memory with 225 individually accessible memory cells in a macroscopic atomic ensemble. As a key element for quantum repeaters, we demonstrate that entanglement with flying optical qubits can be stored into any neighboring memory cells and read out after a programmable time with high fidelity. Experimental realization of a multiplexed quantum memory with many individually accessible memory cells and programmable control of its addressing and readout makes an important step for its application in quantum information technology. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.07267v1-abstract-full').style.display = 'none'; document.getElementById('1707.07267v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 4 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nat. Commun. 8, 15359 (2017) </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

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