CINXE.COM

<!DOCTYPE html> <html lang="en" xmlns:fb="http://www.facebook.com/2008/fbml" class="wf-loading"> <head prefix="og: https://ogp.me/ns# fb: https://ogp.me/ns/fb# academia: https://ogp.me/ns/fb/academia#"> <meta charset="utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta rel="search" type="application/opensearchdescription+xml" href="/open_search.xml" title="Academia.edu"> <title>Bob Coecke | University of Oxford - Academia.edu</title>  <link href="//a.academia-assets.com/images/favicons/favicon-production.ico" rel="shortcut icon" type="image/vnd.microsoft.icon"> <link rel="apple-touch-icon" sizes="57x57" href="//a.academia-assets.com/images/favicons/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon" sizes="60x60" href="//a.academia-assets.com/images/favicons/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon" sizes="72x72" href="//a.academia-assets.com/images/favicons/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon" sizes="76x76" href="//a.academia-assets.com/images/favicons/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon" sizes="114x114" href="//a.academia-assets.com/images/favicons/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon" sizes="120x120" href="//a.academia-assets.com/images/favicons/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon" sizes="144x144" href="//a.academia-assets.com/images/favicons/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon" sizes="152x152" href="//a.academia-assets.com/images/favicons/apple-touch-icon-152x152.png"> <link rel="apple-touch-icon" sizes="180x180" href="//a.academia-assets.com/images/favicons/apple-touch-icon-180x180.png"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-194x194.png" sizes="194x194"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/android-chrome-192x192.png" sizes="192x192"> <link rel="icon" type="image/png" href="//a.academia-assets.com/images/favicons/favicon-16x16.png" sizes="16x16"> <link rel="manifest" href="//a.academia-assets.com/images/favicons/manifest.json"> <meta name="msapplication-TileColor" content="#2b5797"> <meta name="msapplication-TileImage" content="//a.academia-assets.com/images/favicons/mstile-144x144.png"> <meta name="theme-color" content="#ffffff"> <script> window.performance && window.performance.measure && window.performance.measure("Time To First Byte", "requestStart", "responseStart"); </script> <script> (function() { if (!window.URLSearchParams || !window.history || !window.history.replaceState) { return; } var searchParams = new URLSearchParams(window.location.search); var paramsToDelete = [ 'fs', 'sm', 'swp', 'iid', 'nbs', 'rcc', // related content category 'rcpos', // related content carousel position 'rcpg', // related carousel page 'rchid', // related content hit id 'f_ri', // research interest id, for SEO tracking 'f_fri', // featured research interest, for SEO tracking (param key without value) 'f_rid', // from research interest directory for SEO tracking 'f_loswp', // from research interest pills on LOSWP sidebar for SEO tracking 'rhid', // referrring hit id ]; if (paramsToDelete.every((key) => searchParams.get(key) === null)) { return; } paramsToDelete.forEach((key) => { searchParams.delete(key); }); var cleanUrl = new URL(window.location.href); cleanUrl.search = searchParams.toString(); history.replaceState({}, document.title, cleanUrl); })(); </script> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "profiles/works", 'action': "summary", 'controller_action': 'profiles/works#summary', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script type="text/javascript"> window.sendUserTiming = function(timingName) { if (!(window.performance && window.performance.measure)) return; var entries = window.performance.getEntriesByName(timingName, "measure"); if (entries.length !== 1) return; var timingValue = Math.round(entries[0].duration); gtag('event', 'timing_complete', { name: timingName, value: timingValue, event_category: 'User-centric', }); }; window.sendUserTiming("Time To First Byte"); </script> <meta name="csrf-param" content="authenticity_token" /> <meta name="csrf-token" content="3IWma_zYVAUnMbrlh5uBZjc7QYxEtEASAUcMgWGdodhS73YR6tto8-8vabGkinR6TCbJWneS859XoayrQXSOnA" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/wow-3d36c19b4875b226bfed0fcba1dcea3f2fe61148383d97c0465c016b8c969290.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/social/home-79e78ce59bef0a338eb6540ec3d93b4a7952115b56c57f1760943128f4544d42.css" /><script type="application/ld+json">{"@context":"https://schema.org","@type":"ProfilePage","mainEntity":{"@context":"https://schema.org","@type":"Person","name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"dateCreated":"2010-01-08T18:32:13-08:00","dateModified":"2023-02-13T03:00:19-08:00"}</script><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/heading-95367dc03b794f6737f30123738a886cf53b7a65cdef98a922a98591d60063e3.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/button-8c9ae4b5c8a2531640c354d92a1f3579c8ff103277ef74913e34c8a76d4e6c00.css" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/body-170d1319f0e354621e81ca17054bb147da2856ec0702fe440a99af314a6338c5.css" /><link crossorigin="" href="https://fonts.gstatic.com/" rel="preconnect" /><link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,opsz,wght@0,9..40,100..1000;1,9..40,100..1000&family=Gupter:wght@400;500;700&family=IBM+Plex+Mono:wght@300;400&family=Material+Symbols+Outlined:opsz,wght,FILL,GRAD@20,400,0,0&display=swap" rel="stylesheet" /><link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system/common-2b6f90dbd75f5941bc38f4ad716615f3ac449e7398313bb3bc225fba451cd9fa.css" /> <meta name="author" content="bob coecke" /> <meta name="description" content="I am Chief Scientist at Quantinuum, head Quantinuum's Oxford-based Quantum NLP & Compositional Intelligence sub-team, Distinguished Visiting Research Chair at…" /> <meta name="google-site-verification" content="bKJMBZA7E43xhDOopFZkssMMkBRjvYERV-NaN4R6mrs" /> <script> var $controller_name = 'works'; var $action_name = "summary"; var $rails_env = 'production'; var $app_rev = '1e60a92a442ff83025cbe4f252857ee7c49c0bbe'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.Aedu = { hit_data: null }; window.Aedu.SiteStats = {"premium_universities_count":14008,"monthly_visitors":"107 million","monthly_visitor_count":107440917,"monthly_visitor_count_in_millions":107,"user_count":283736681,"paper_count":55203019,"paper_count_in_millions":55,"page_count":432000000,"page_count_in_millions":432,"pdf_count":16500000,"pdf_count_in_millions":16}; window.Aedu.serverRenderTime = new Date(1740549509000); window.Aedu.timeDifference = new Date().getTime() - 1740549509000; window.Aedu.isUsingCssV1 = false; window.Aedu.enableLocalization = true; window.Aedu.activateFullstory = false; window.Aedu.serviceAvailability = { status: {"attention_db":"on","bibliography_db":"on","contacts_db":"on","email_db":"on","indexability_db":"on","mentions_db":"on","news_db":"on","notifications_db":"on","offsite_mentions_db":"on","redshift":"on","redshift_exports_db":"on","related_works_db":"on","ring_db":"on","user_tests_db":"on"}, serviceEnabled: function(service) { return this.status[service] === "on"; }, readEnabled: function(service) { return this.serviceEnabled(service) || this.status[service] === "read_only"; }, }; window.Aedu.viewApmTrace = function() { // Check if x-apm-trace-id meta tag is set, and open the trace in APM // in a new window if it is. var apmTraceId = document.head.querySelector('meta[name="x-apm-trace-id"]'); if (apmTraceId) { var traceId = apmTraceId.content; // Use trace ID to construct URL, an example URL looks like: // https://app.datadoghq.com/apm/traces?query=trace_id%31298410148923562634 var apmUrl = 'https://app.datadoghq.com/apm/traces?query=trace_id%3A' + traceId; window.open(apmUrl, '_blank'); } }; </script>  <link href="https://fonts.googleapis.com/css?family=Roboto:100,100i,300,300i,400,400i,500,500i,700,700i,900,900i" rel="stylesheet"> <link rel="preload" href="//maxcdn.bootstrapcdn.com/font-awesome/4.3.0/css/font-awesome.min.css" as="style" onload="this.rel='stylesheet'"> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/libraries-a9675dcb01ec4ef6aa807ba772c7a5a00c1820d3ff661c1038a20f80d06bb4e4.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/academia-1eb081e01ca8bc0c1b1d866df79d9eb4dd2c484e4beecf76e79a7806c72fee08.css" /> <link rel="stylesheet" media="all" href="//a.academia-assets.com/assets/design_system_legacy-056a9113b9a0f5343d013b29ee1929d5a18be35fdcdceb616600b4db8bd20054.css" /> <script src="//a.academia-assets.com/assets/webpack_bundles/runtime-bundle-005434038af4252ca37c527588411a3d6a0eabb5f727fac83f8bbe7fd88d93bb.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/webpack_libraries_and_infrequently_changed.wjs-bundle-63c3b84e278fb86e50772ccc2ac0281a0f74ac7e2f88741ecad58131583d4c47.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/core_webpack.wjs-bundle-85b27a68dc793256271cea8ce6f178025923f9e7e3c7450780e59eacecf59a75.js"></script> <script src="//a.academia-assets.com/assets/webpack_bundles/sentry.wjs-bundle-5fe03fddca915c8ba0f7edbe64c194308e8ce5abaed7bffe1255ff37549c4808.js"></script> <script> jade = window.jade || {}; jade.helpers = window.$h; jade._ = window._; </script>  <script id="tag-manager-head-root">(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer_old','GTM-5G9JF7Z');</script>  <script> window.gptadslots = []; window.googletag = window.googletag || {}; window.googletag.cmd = window.googletag.cmd || []; </script> <script type="text/javascript"> // TODO(jacob): This should be defined, may be rare load order problem. // Checking if null is just a quick fix, will default to en if unset. // Better fix is to run this immedietely after I18n is set. if (window.I18n != null) { I18n.defaultLocale = "en"; I18n.locale = "en"; I18n.fallbacks = true; } </script> <link rel="canonical" href="https://oxford.academia.edu/BobCoecke" /> </head>   <body class='c-profiles/works a-summary logged_out'>  <div id="fb-root"></div><script>window.fbAsyncInit = function() { FB.init({ appId: "2369844204", version: "v8.0", status: true, cookie: true, xfbml: true }); // Additional initialization code. if (window.InitFacebook) { // facebook.ts already loaded, set it up. window.InitFacebook(); } else { // Set a flag for facebook.ts to find when it loads. window.academiaAuthReadyFacebook = true; } };</script><script>window.fbAsyncLoad = function() { // Protection against double calling of this function if (window.FB) { return; } (function(d, s, id){ var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) {return;} js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_US/sdk.js"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk')); } if (!window.defer_facebook) { // Autoload if not deferred window.fbAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.fbAsyncLoad(); }, 5000); }</script> <div id="google-root"></div><script>window.loadGoogle = function() { if (window.InitGoogle) { // google.ts already loaded, set it up. window.InitGoogle("331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"); } else { // Set a flag for google.ts to use when it loads. window.GoogleClientID = "331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b"; } };</script><script>window.googleAsyncLoad = function() { // Protection against double calling of this function (function(d) { var js; var id = 'google-jssdk'; var ref = d.getElementsByTagName('script')[0]; if (d.getElementById(id)) { return; } js = d.createElement('script'); js.id = id; js.async = true; js.onload = loadGoogle; js.src = "https://accounts.google.com/gsi/client" ref.parentNode.insertBefore(js, ref); }(document)); } if (!window.defer_google) { // Autoload if not deferred window.googleAsyncLoad(); } else { // Defer loading by 5 seconds setTimeout(function() { window.googleAsyncLoad(); }, 5000); }</script> <div id="tag-manager-body-root">  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-5G9JF7Z" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>   <script> window.addEventListener('load', function() { if (document.querySelector('input[name="commit"]')) { document.querySelector('input[name="commit"]').addEventListener('click', function() { gtag('event', 'click', { event_category: 'button', event_label: 'Log In' }) }) } }); </script> </div> <script>var _comscore = _comscore || []; _comscore.push({ c1: "2", c2: "26766707" }); (function() { var s = document.createElement("script"), el = document.getElementsByTagName("script")[0]; s.async = true; s.src = (document.location.protocol == "https:" ? "https://sb" : "http://b") + ".scorecardresearch.com/beacon.js"; el.parentNode.insertBefore(s, el); })();</script><img src="https://sb.scorecardresearch.com/p?c1=2&c2=26766707&cv=2.0&cj=1" style="position: absolute; visibility: hidden" /> <div id='react-modal'></div> <div class='DesignSystem'> <a class='u-showOnFocus' href='#site'> Skip to main content </a> </div> <div id="upgrade_ie_banner" style="display: none;"><p>Academia.edu no longer supports Internet Explorer.</p><p>To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to <a href="https://www.academia.edu/upgrade-browser">upgrade your browser</a>.</p></div><script>// Show this banner for all versions of IE if (!!window.MSInputMethodContext || /(MSIE)/.test(navigator.userAgent)) { document.getElementById('upgrade_ie_banner').style.display = 'block'; }</script> <div class="DesignSystem bootstrap ShrinkableNav"><div class="navbar navbar-default main-header"><div class="container-wrapper" id="main-header-container"><div class="container"><div class="navbar-header"><div class="nav-left-wrapper u-mt0x"><div class="nav-logo"><a data-main-header-link-target="logo_home" href="https://www.academia.edu/"><img class="visible-xs-inline-block" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015-A.svg" width="24" height="24" /><img width="145.2" height="18" class="hidden-xs" style="height: 24px;" alt="Academia.edu" src="//a.academia-assets.com/images/academia-logo-redesign-2015.svg" /></a></div><div class="nav-search"><div class="SiteSearch-wrapper select2-no-default-pills"><form class="js-SiteSearch-form DesignSystem" action="https://www.academia.edu/search" accept-charset="UTF-8" method="get"><i class="SiteSearch-icon fa fa-search u-fw700 u-positionAbsolute u-tcGrayDark"></i><input class="js-SiteSearch-form-input SiteSearch-form-input form-control" data-main-header-click-target="search_input" name="q" placeholder="Search" type="text" value="" /></form></div></div></div><div class="nav-right-wrapper pull-right"><ul class="NavLinks js-main-nav list-unstyled"><li class="NavLinks-link"><a class="js-header-login-url Button Button--inverseGray Button--sm u-mb4x" id="nav_log_in" rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="NavLinks-link u-p0x"><a class="Button Button--inverseGray Button--sm u-mb4x" rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li></ul><button class="hidden-lg hidden-md hidden-sm u-ml4x navbar-toggle collapsed" data-target=".js-mobile-header-links" data-toggle="collapse" type="button"><span class="icon-bar"></span><span class="icon-bar"></span><span class="icon-bar"></span></button></div></div><div class="collapse navbar-collapse js-mobile-header-links"><ul class="nav navbar-nav"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/login">Log In</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/signup">Sign Up</a></li><li class="u-borderColorGrayLight u-borderBottom1 js-mobile-nav-expand-trigger"><a href="#">more&nbsp<span class="caret"></span></a></li><li><ul class="js-mobile-nav-expand-section nav navbar-nav u-m0x collapse"><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/about">About</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/press">Press</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="false" href="https://www.academia.edu/documents">Papers</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://www.academia.edu/hiring"><i class="fa fa-briefcase"></i> We're Hiring!</a></li><li class="u-borderColorGrayLight u-borderBottom1"><a rel="nofollow" href="https://support.academia.edu/hc/en-us"><i class="fa fa-question-circle"></i> Help Center</a></li><li class="js-mobile-nav-collapse-trigger u-borderColorGrayLight u-borderBottom1 dropup" style="display:none"><a href="#">less&nbsp<span class="caret"></span></a></li></ul></li></ul></div></div></div><script>(function(){ var $moreLink = $(".js-mobile-nav-expand-trigger"); var $lessLink = $(".js-mobile-nav-collapse-trigger"); var $section = $('.js-mobile-nav-expand-section'); $moreLink.click(function(ev){ ev.preventDefault(); $moreLink.hide(); $lessLink.show(); $section.collapse('show'); }); $lessLink.click(function(ev){ ev.preventDefault(); $moreLink.show(); $lessLink.hide(); $section.collapse('hide'); }); })() if ($a.is_logged_in() || false) { new Aedu.NavigationController({ el: '.js-main-nav', showHighlightedNotification: false }); } else { $(".js-header-login-url").attr("href", $a.loginUrlWithRedirect()); } Aedu.autocompleteSearch = new AutocompleteSearch({el: '.js-SiteSearch-form'});</script></div></div> <div id='site' class='fixed'> <div id="content" class="clearfix"> <script>document.addEventListener('DOMContentLoaded', function(){ var $dismissible = $(".dismissible_banner"); $dismissible.click(function(ev) { $dismissible.hide(); }); });</script> <script src="//a.academia-assets.com/assets/webpack_bundles/profile.wjs-bundle-4a9f418052ec7a403e004849742322653b010f552f60e892779ac5b03c4cc162.js" defer="defer"></script><script>$viewedUser = Aedu.User.set_viewed( {"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke","photo":"https://0.academia-photos.com/112917/30501/94990939/s65_bob.coecke.jpg","has_photo":true,"department":{"id":178297,"name":"Department of Computer Science","url":"https://oxford.academia.edu/Departments/Department_of_Computer_Science/Documents","university":{"id":33,"name":"University of Oxford","url":"https://oxford.academia.edu/"}},"position":"Emeritus","position_id":6,"is_analytics_public":false,"interests":[{"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":1200,"name":"Languages and Linguistics","url":"https://www.academia.edu/Documents/in/Languages_and_Linguistics"},{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"}]} ); if ($a.is_logged_in() && $viewedUser.is_current_user()) { $('body').addClass('profile-viewed-by-owner'); } $socialProfiles = [{"id":168935,"link":"http://www.cs.ox.ac.uk/people/bob.coecke/","name":"Homepage","link_domain":"www.cs.ox.ac.uk","icon":"//www.google.com/s2/u/0/favicons?domain=www.cs.ox.ac.uk"},{"id":69578386,"link":"https://www.quantinuum.com/qai/bobcoecke","name":"Homepage","link_domain":"www.quantinuum.com","icon":"//www.google.com/s2/u/0/favicons?domain=www.quantinuum.com"},{"id":69578394,"link":"https://twitter.com/coecke","name":"Twitter","link_domain":"twitter.com","icon":"//www.google.com/s2/u/0/favicons?domain=twitter.com"},{"id":69578402,"link":"https://www.linkedin.com/in/bob-coecke-9389627/","name":"Linkedin","link_domain":"www.linkedin.com","icon":"//www.google.com/s2/u/0/favicons?domain=www.linkedin.com"},{"id":69578413,"link":"https://scholar.google.com/citations?user=fO17CXgAAAAJ\u0026hl=en","name":"Google Scholar","link_domain":"scholar.google.com","icon":"//www.google.com/s2/u/0/favicons?domain=scholar.google.com"}]</script><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://oxford.academia.edu/BobCoecke","location":"/BobCoecke","scheme":"https","host":"oxford.academia.edu","port":null,"pathname":"/BobCoecke","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="ProfileCheckPaperUpdate" data-props="{}" data-trace="false" data-dom-id="ProfileCheckPaperUpdate-react-component-77d48f06-bed6-47d8-80ef-f6dea644f2ca"></div> <div id="ProfileCheckPaperUpdate-react-component-77d48f06-bed6-47d8-80ef-f6dea644f2ca"></div> <div class="DesignSystem"><div class="onsite-ping" id="onsite-ping"></div></div><div class="profile-user-info DesignSystem"><div class="social-profile-container"><div class="left-panel-container"><div class="user-info-component-wrapper"><div class="user-summary-cta-container"><div class="user-summary-container"><div class="social-profile-avatar-container"><img class="profile-avatar u-positionAbsolute" alt="Bob Coecke" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/112917/30501/94990939/s200_bob.coecke.jpg" /></div><div class="title-container"><h1 class="ds2-5-heading-sans-serif-sm">Bob Coecke</h1><div class="affiliations-container fake-truncate js-profile-affiliations"><div><a class="u-tcGrayDarker" href="https://oxford.academia.edu/">University of Oxford</a>, <a class="u-tcGrayDarker" href="https://oxford.academia.edu/Departments/Department_of_Computer_Science/Documents">Department of Computer Science</a>, <span class="u-tcGrayDarker">Emeritus</span></div><div><a class="u-tcGrayDarker" href="https://perimeterinstitute.academia.edu/">Perimeter Institute for Theoretical Physics</a>, <a class="u-tcGrayDarker" href="https://perimeterinstitute.academia.edu/Departments/Quantum_Foundations/Documents">Quantum Foundations</a>, <span class="u-tcGrayDarker">Distinguished Visiting Research Chair</span></div></div></div></div><div class="sidebar-cta-container"><button class="ds2-5-button hidden profile-cta-button grow js-profile-follow-button" data-broccoli-component="user-info.follow-button" data-click-track="profile-user-info-follow-button" data-follow-user-fname="Bob" data-follow-user-id="112917" data-follow-user-source="profile_button" data-has-google="false"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">add</span>Follow</button><button class="ds2-5-button hidden profile-cta-button grow js-profile-unfollow-button" data-broccoli-component="user-info.unfollow-button" data-click-track="profile-user-info-unfollow-button" data-unfollow-user-id="112917"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">done</span>Following</button></div></div><div class="user-stats-container"><a><div class="stat-container js-profile-followers"><p class="label">Followers</p><p class="data">317</p></div></a><a><div class="stat-container js-profile-followees" data-broccoli-component="user-info.followees-count" data-click-track="profile-expand-user-info-following"><p class="label">Following</p><p class="data">151</p></div></a><a><div class="stat-container js-profile-coauthors" data-broccoli-component="user-info.coauthors-count" data-click-track="profile-expand-user-info-coauthors"><p class="label">Co-authors</p><p class="data">13</p></div></a><div class="js-mentions-count-container" style="display: none;"><a href="/BobCoecke/mentions"><div class="stat-container"><p class="label">Mentions</p><p class="data"></p></div></a></div><span><div class="stat-container"><p class="label"><span class="js-profile-total-view-text">Public Views</span></p><p class="data"><span class="js-profile-view-count"></span></p></div></span></div><div class="user-bio-container"><div class="profile-bio fake-truncate js-profile-about" style="margin: 0px;">I am Chief Scientist at Quantinuum, head Quantinuum's Oxford-based Quantum NLP & Compositional Intelligence sub-team, Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics, Emeritus Fellow at Wolfson College Oxford, and Visiting Fellow at the Computer Science Department and the Mathematical Institute of Oxford University. Previously I was Professor of Quantum Foundations, Logics and Structures at the Department of Computer Science at Oxford University, where I was 20 years, and co-founded and led a multi-disciplinary Quantum Group that grew to 50 members and I supervised close to 70 PhD students. I am still supervising, at Oxford and elsewhere, and also still teach at Oxford's Mathematical Institute. I pioneered Categorical Quantum Mechanics (now in AMS's MSC2020 classification), ZX-calculus, DisCoCat natural language meaning, mathematical foundations for resource theories, Quantum Natural Language Processing, and DisCoCirc natural language meaning. I co-authored Picturing Quantum Processes, with Aleks Kissinger, a book providing a fully diagrammatic treatment of quantum theory and its applications. I co-authored Quantum in Pictures, with Stefano Gogioso, which does the same, but now accessible to people with no maths background. I co-authored some 200 research papers. I obtained approx. 35 grants, including from NFWO, EPSRC, Leverhulme, EU, ONR, AFOSR, FQXi, JTF. I still hold grants with the latter two. I am a founding father of the QPL (Quantum Physics and Logic) and ACT (Applied Category Theory) communities, of the diamond-open-access journal Compositionality, and Cambridge University Press' Applied Category Theory book series. I was the first person to have Quantum Foundations as part of his academic title. My work has been headlined by various media outlets, including Forbes, New Scientist, PhysicsWorld, ComputerWeekly.<br /><span class="u-fw700">Phone: </span>+44 7881 333990<br /><b>Address: </b>Quantinuum (Oxford Campus), 17 Beaumont Street, OX1 2NA Oxford, UK.<br /><div class="js-profile-less-about u-linkUnstyled u-tcGrayDarker u-textDecorationUnderline u-displayNone">less</div></div></div><div class="suggested-academics-container"><div class="suggested-academics--header"><p class="ds2-5-body-md-bold">Related Authors</p></div><ul class="suggested-user-card-list"><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://utexas.academia.edu/NaamaPatEl"><img class="profile-avatar u-positionAbsolute" alt="Na'ama Pat-El" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/14496/4846/4740/s200_na_ama.pat-el.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://utexas.academia.edu/NaamaPatEl">Na'ama Pat-El</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">The University of Texas at Austin</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://unizg.academia.edu/AndrejDujella"><img class="profile-avatar u-positionAbsolute" alt="Andrej Dujella" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/29857/9709/9189/s200_andrej.dujella.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://unizg.academia.edu/AndrejDujella">Andrej Dujella</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Zagreb</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://cria.academia.edu/ArmandoMarquesGuedes"><img class="profile-avatar u-positionAbsolute" alt="Armando Marques-Guedes" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/134181/3401094/148494125/s200_armando.marques-guedes.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://cria.academia.edu/ArmandoMarquesGuedes">Armando Marques-Guedes</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">UNL - New University of Lisbon</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://huji.academia.edu/EitanGrossman"><img class="profile-avatar u-positionAbsolute" alt="Eitan Grossman" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/165093/41884/64625709/s200_eitan.grossman.jpeg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://huji.academia.edu/EitanGrossman">Eitan Grossman</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">The Hebrew University of Jerusalem</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://eva-mpg.academia.edu/MartinHaspelmath"><img class="profile-avatar u-positionAbsolute" alt="Martin Haspelmath" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/187373/89901/92584166/s200_martin.haspelmath.png" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://eva-mpg.academia.edu/MartinHaspelmath">Martin Haspelmath</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Max Planck Institute for Evolutionary Anthropology</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://ncit.academia.edu/RoshanChitrakar"><img class="profile-avatar u-positionAbsolute" alt="Roshan Chitrakar" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/371695/9733675/15833098/s200_roshan.chitrakar.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://ncit.academia.edu/RoshanChitrakar">Roshan Chitrakar</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Nepal College of Information Technology</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://gc-cuny.academia.edu/LevManovich"><img class="profile-avatar u-positionAbsolute" alt="Lev Manovich" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/412778/130321/66062342/s200_lev.manovich.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://gc-cuny.academia.edu/LevManovich">Lev Manovich</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">Graduate Center of the City University of New York</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://illinois.academia.edu/KiranDasari"><img class="profile-avatar u-positionAbsolute" alt="Kiran Dasari" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/1693440/585320/3191167/s200_kiran.dasari.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://illinois.academia.edu/KiranDasari">Kiran Dasari</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">University of Illinois at Urbana-Champaign</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://rivpolyonline.academia.edu/PALIMOTEJUSTICE"><img class="profile-avatar u-positionAbsolute" alt="PALIMOTE JUSTICE" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/5326299/2340125/24766135/s200_justice.palimote.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://rivpolyonline.academia.edu/PALIMOTEJUSTICE">PALIMOTE JUSTICE</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">RIVERS STATE POLYTECHNIC</p></div></div><div class="suggested-user-card"><div class="suggested-user-card__avatar social-profile-avatar-container"><a href="https://djasljsa.academia.edu/AdnanAwad"><img class="profile-avatar u-positionAbsolute" alt="Adnan Awad" border="0" onerror="if (this.src != '//a.academia-assets.com/images/s200_no_pic.png') this.src = '//a.academia-assets.com/images/s200_no_pic.png';" width="200" height="200" src="https://0.academia-photos.com/17255937/5084286/5829848/s200_adnan.awad.jpg" /></a></div><div class="suggested-user-card__user-info"><a class="suggested-user-card__user-info__header ds2-5-body-sm-bold ds2-5-body-link" href="https://djasljsa.academia.edu/AdnanAwad">Adnan Awad</a><p class="suggested-user-card__user-info__subheader ds2-5-body-xs">The University Of Jordan</p></div></div></ul></div><div class="ri-section"><div class="ri-section-header"><span>Interests</span></div><div class="ri-tags-container"><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="112917" href="https://www.academia.edu/Documents/in/Computer_Science"><div id="js-react-on-rails-context" style="display:none" data-rails-context="{"inMailer":false,"i18nLocale":"en","i18nDefaultLocale":"en","href":"https://oxford.academia.edu/BobCoecke","location":"/BobCoecke","scheme":"https","host":"oxford.academia.edu","port":null,"pathname":"/BobCoecke","search":null,"httpAcceptLanguage":null,"serverSide":false}"></div> <div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Computer Science"]}" data-trace="false" data-dom-id="Pill-react-component-a81b3862-70b9-44e8-93ea-e876562846f3"></div> <div id="Pill-react-component-a81b3862-70b9-44e8-93ea-e876562846f3"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="112917" href="https://www.academia.edu/Documents/in/Physics"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Physics"]}" data-trace="false" data-dom-id="Pill-react-component-a3e6b939-5f7e-48f3-a407-94497c4580c6"></div> <div id="Pill-react-component-a3e6b939-5f7e-48f3-a407-94497c4580c6"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="112917" href="https://www.academia.edu/Documents/in/Languages_and_Linguistics"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Languages and Linguistics"]}" data-trace="false" data-dom-id="Pill-react-component-44721808-a80b-452b-b261-3fba4b4c13b2"></div> <div id="Pill-react-component-44721808-a80b-452b-b261-3fba4b4c13b2"></div> </a><a data-click-track="profile-user-info-expand-research-interests" data-has-card-for-ri-list="112917" href="https://www.academia.edu/Documents/in/Mathematics"><div class="js-react-on-rails-component" style="display:none" data-component-name="Pill" data-props="{"color":"gray","children":["Mathematics"]}" data-trace="false" data-dom-id="Pill-react-component-eaa5c652-646c-444a-a8ec-aa8434d88ae1"></div> <div id="Pill-react-component-eaa5c652-646c-444a-a8ec-aa8434d88ae1"></div> </a></div></div><div class="external-links-container"><ul class="profile-links new-profile js-UserInfo-social"><li class="profile-profiles js-social-profiles-container"><i class="fa fa-spin fa-spinner"></i></li></ul></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 Bob Coecke</h3></div><div class="js-work-strip profile--work_container" data-work-id="94621890"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift"><img alt="Research paper thumbnail of Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift">Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="94621890"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621890"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621890; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621890]").text(description); $(".js-view-count[data-work-id=94621890]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621890; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621890']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621890]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621890,"title":"Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift","internal_url":"https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621889"><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/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits"><img alt="Research paper thumbnail of Tutorial: Graphical Calculus for Quantum Circuits" class="work-thumbnail" src="https://attachments.academia-assets.com/97028021/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/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits">Tutorial: Graphical Calculus for Quantum Circuits</a></div><div class="wp-workCard_item"><span>Reversible Computation</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We explain the graphical zx-calculus for reasoning about qubits without any reference to the unde...</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 explain the graphical zx-calculus for reasoning about qubits without any reference to the underlying categorical semantics, and illustrate its use on quantum circuits.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f37695b86b4d1897c363fc45e52ad3d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97028021,"asset_id":94621889,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97028021/download_file?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="94621889"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621889"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621889; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621889]").text(description); $(".js-view-count[data-work-id=94621889]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621889; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621889']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "9f37695b86b4d1897c363fc45e52ad3d" } } $('.js-work-strip[data-work-id=94621889]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621889,"title":"Tutorial: Graphical Calculus for Quantum Circuits","internal_url":"https://www.academia.edu/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97028021,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97028021/thumbnails/1.jpg","file_name":"978-3-642-36315-3_1.pdf","download_url":"https://www.academia.edu/attachments/97028021/download_file","bulk_download_file_name":"Tutorial_Graphical_Calculus_for_Quantum.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97028021/978-3-642-36315-3_1-libre.pdf?1673266130=\u0026response-content-disposition=attachment%3B+filename%3DTutorial_Graphical_Calculus_for_Quantum.pdf\u0026Expires=1740553109\u0026Signature=Qz27gVaMKpjQUwX3LplHcQ8sTJQyBW32MAalIJYnplZx5zyEJbjZ-f-heFwq8qy4kU64wrC1xviQGdq2lrmXWNzwjqH2Sd9WZfKAMonCNUGNwwDBGeVnDvNbUJBu~u53qgWU7Ox4BxLbFFs6LSi0Vtju~5vJjnHJsMai25yKluZBwIjl3h-FfQGfgdhI~n36A7EJHn1iqA3ON-0Uh-6ba7lVSmIrIK7spUV3kYGQqcbCodIYS40N9Yy22dOMClbKzC2lShh7alxdMAxD62r95r47RW9GctmG-1Oc2EAkCOIRwwS0E~amrY0ymMvn4KyLylnt3QxsuAccxiYyAujVWg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="94621888"><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/94621888/Partiality_in_physics"><img alt="Research paper thumbnail of Partiality in physics" class="work-thumbnail" src="https://attachments.academia-assets.com/97028004/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/94621888/Partiality_in_physics">Partiality in physics</a></div><div class="wp-workCard_item"><span>Computing Research Repository - CORR</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We revisit the standard axioms of domain theory with emphasis on their relation to the concept of...</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 revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting capable of providing a satisfactory unification of the two. finite string is partial, the infinite strings are total. In the domain (IR, ⊑), the collection of compact intervals (a, b) of the real line ordered by reverse inclusion, an interval like (p, q) with p &lt; q rational is partial, while a one point interval (x) representing a real number is total. In the domain (n, ⊑), the n dimensional mixed states in the spectral order (to be defined later), a pure state is total, while mixed states which are not pure are partial. In all the cases above, total elements coincide with elements which are maximal in the given order. As we can see, the partiality idea arises naturally in both computer science and physics. The idea is important in computer scienc...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="70e1b47d269510b013da78da9729ae08" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97028004,"asset_id":94621888,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97028004/download_file?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="94621888"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621888"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621888; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621888]").text(description); $(".js-view-count[data-work-id=94621888]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621888; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621888']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "70e1b47d269510b013da78da9729ae08" } } $('.js-work-strip[data-work-id=94621888]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621888,"title":"Partiality in physics","internal_url":"https://www.academia.edu/94621888/Partiality_in_physics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97028004,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97028004/thumbnails/1.jpg","file_name":"0312044v1.pdf","download_url":"https://www.academia.edu/attachments/97028004/download_file","bulk_download_file_name":"Partiality_in_physics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97028004/0312044v1-libre.pdf?1673266136=\u0026response-content-disposition=attachment%3B+filename%3DPartiality_in_physics.pdf\u0026Expires=1740553109\u0026Signature=fw2o1lVB4hxni3XkKzWLzkrC3F0y-7iKlbv4XLoETieKwFankrvpM7D0apN6twGWsJ5YAuWnbRh65UFnlLGzoLoklLFAlQuA4mYi~s7Low0jvWkhZj1KLUpLVWxCl9og8Q79r-VbiDn649KMSYHMyzQE0WaFUGj1~ZyMlt14QZAhwff~JzmTXHgcxm5WESZ3L0Jvi9r7AxK0o1H9wK7xdWNC2MkrAyVyZ9vUf61MQiIqySXO5jP6HPA~jX7ZYkEPXST3H77wlyG9zNZwF0tY4mcrctEWzNavLG2G9Sd3jqUyYq~zW37MYvPUT1d52RGONJe5YAhD2fv5O8jU2QH5sg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="94621887"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics"><img alt="Research paper thumbnail of Domain theory and quantum mechanics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics">Domain theory and quantum mechanics</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce a partial order on classical and quantum states which reveals that these sets are ac...</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 introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same way that the order on a domain provides a rigorous qualitative definition of information, a special type of mapping on a domain called a measurement provides a formal account of ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="94621887"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621887"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621887; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621887]").text(description); $(".js-view-count[data-work-id=94621887]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621887; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621887']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621887]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621887,"title":"Domain theory and quantum mechanics","internal_url":"https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621886"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_"><img alt="Research paper thumbnail of Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_">Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)</a></div><div class="wp-workCard_item"><span>QPL 2011</span><span>, Oct 27, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This position paper serves two purposes:(1) In the light of recent reconstructions of quantum the...</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 position paper serves two purposes:(1) In the light of recent reconstructions of quantum theory, this paper shows the need for a representation theorem for categorical quantum mechanics (CQM), which establishes how conceptually-meaningful constructions on processes and their compositions lead to Hilbert space structure, without any reference of instrumentalist concepts such as measurement.(2) As a first step towards this goal we show how several of the instrumentalist principles underpinning Pavia&#x27;s reconstruction of finitary ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="94621886"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621886"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621886; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621886]").text(description); $(".js-view-count[data-work-id=94621886]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621886; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621886']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621886]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621886,"title":"Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)","internal_url":"https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621885"><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/94621885/Toy_quantum_categories"><img alt="Research paper thumbnail of Toy quantum categories" class="work-thumbnail" src="https://attachments.academia-assets.com/97027924/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/94621885/Toy_quantum_categories">Toy quantum categories</a></div><div class="wp-workCard_item"><span>Electronic notes in theoretical computer science</span><span>, Feb 10, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that Rob Spekken&#x27;s toy quantum theory arises as an instance of our categorical appro...</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 that Rob Spekken&#x27;s toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="450a93f09f2b62055b45465b46113ee9" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97027924,"asset_id":94621885,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97027924/download_file?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="94621885"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621885"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621885; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621885]").text(description); $(".js-view-count[data-work-id=94621885]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621885; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621885']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "450a93f09f2b62055b45465b46113ee9" } } $('.js-work-strip[data-work-id=94621885]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621885,"title":"Toy quantum categories","internal_url":"https://www.academia.edu/94621885/Toy_quantum_categories","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97027924,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97027924/thumbnails/1.jpg","file_name":"0808.pdf","download_url":"https://www.academia.edu/attachments/97027924/download_file","bulk_download_file_name":"Toy_quantum_categories.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97027924/0808-libre.pdf?1673266138=\u0026response-content-disposition=attachment%3B+filename%3DToy_quantum_categories.pdf\u0026Expires=1740553109\u0026Signature=Yq8un8yRz1O8uJ2Is6Av1YO2pdgw3rN~W54-36P851OyUciXvpqPUbXp0if1DkVDC6IFHvazf48zjeXIUd7IvL6Rk5MtECULCa-R-MuR0DLUG6eeIhHJ0paJi-RfIoUHZWAGw0Tz34-v~q4rXmQKUqSk4wwxt6aNoxCcnj8XocP2lIvaZGc4qoulD4YQ5muRb50bA6y7ydX4tp0NShZLZYbBuQiltDAuO0eKilmCJJHnNhO-Y5mG8urSaqJ1O2rPMz6zLku0EWMN3PKnnPNgj-5b25U30Ygpsj9nwErseFqdlJo5X2ULnaxs~xsg5R-B4x1vI631J3L8iz0w7huvtg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983362"><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/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement"><img alt="Research paper thumbnail of The Compositional Structure of Multipartite Quantum Entanglement" class="work-thumbnail" src="https://attachments.academia-assets.com/90535223/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/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement">The Compositional Structure of Multipartite Quantum Entanglement</a></div><div class="wp-workCard_item"><span>Automata, Languages and Programming</span><span>, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">While multipartite quantum states constitute a (if not the) key resource for quantum computations...</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">While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a high-level, structural understanding of entanglement involving arbitrarily many qubits is a longstanding open problem in quantum computer science. In this paper we expose the algebraic and graphical structure of the GHZ-state and the W-state, as well as a purely graphical distinction that characterises the behaviours of these states. In turn, this structure yields a compositional graphical model for expressing general multipartite states. We identify those states, named Frobenius states, which canonically induce an algebraic structure, namely the structure of a commutative Frobenius algebra (CFA). We show that all SLOCC-maximal tripartite qubit states are locally equivalent to Frobenius states. Those that are SLOCC-equivalent to the GHZ-state induce special commutative Frobenius algebras, while those that are SLOCC-equivalent to the W-state induce what we call anti-special commutative Frobenius algebras. From the SLOCC-classification of tripartite qubit states follows a representation theorem for two dimensional CFAs. Together, a GHZ and a W Frobenius state form the primitives of a graphical calculus. This calculus is expressive enough to generate and reason about arbitrary multipartite states, which are obtained by "composing" the GHZ-and W-states, giving rise to a rich graphical paradigm for general multipartite entanglement.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7d1de0961e86dc0300e243e6ee62f59a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535223,"asset_id":85983362,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535223/download_file?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="85983362"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983362"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983362; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983362]").text(description); $(".js-view-count[data-work-id=85983362]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983362; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983362']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "7d1de0961e86dc0300e243e6ee62f59a" } } $('.js-work-strip[data-work-id=85983362]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983362,"title":"The Compositional Structure of Multipartite Quantum Entanglement","internal_url":"https://www.academia.edu/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535223,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535223/thumbnails/1.jpg","file_name":"1002.pdf","download_url":"https://www.academia.edu/attachments/90535223/download_file","bulk_download_file_name":"The_Compositional_Structure_of_Multipart.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535223/1002-libre.pdf?1662037467=\u0026response-content-disposition=attachment%3B+filename%3DThe_Compositional_Structure_of_Multipart.pdf\u0026Expires=1740553109\u0026Signature=TXEh6FX8BP8~l9X6bDYWW-9kcBSP6nLmWHL677eMNBiMfaSKfP-xCaRneUe1QNo-JDOn9ggWOI9v-4gTU6~OER9EE~ZpunxoR5ZtFqahncMbQBxzpHKZJuC~a~YJMCXZ-XFkG-pvFzuDYwMZarl~L-i1bLxeJTuqtMKgWYcgDlZPhEwY5Q0Jy61SkQ0~E1qWa98ZXNU3vft65qK4fRmkUwS6R~ud8BDECu~sOmdXJ~PRhhHD1jsMz5I8Idcz5bMYpiQKZk4aI1rQY1zwhjlvy62jk6TJZjoKzrQ9JBHRhq7x9Wwz4OaDw7IiEHsam-3VJM9g3QWk8IOz93J2h-i2kw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983356"><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/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach"><img alt="Research paper thumbnail of Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach" class="work-thumbnail" src="https://attachments.academia-assets.com/90535211/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/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach">Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach</a></div><div class="wp-workCard_item"><span>Metadebates on Science</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It will be shown in this article that an ontological approach for some problems related to the in...</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">It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing "space" as the seat of stability, and "time" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1ebb2a49fdb3ccc1021fce5c10b273cf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535211,"asset_id":85983356,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535211/download_file?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="85983356"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983356"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983356; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983356]").text(description); $(".js-view-count[data-work-id=85983356]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983356; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983356']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "1ebb2a49fdb3ccc1021fce5c10b273cf" } } $('.js-work-strip[data-work-id=85983356]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983356,"title":"Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach","translated_title":"","metadata":{"grobid_abstract":"It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing \"space\" as the seat of stability, and \"time\" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Metadebates on Science","grobid_abstract_attachment_id":90535211},"translated_abstract":null,"internal_url":"https://www.academia.edu/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach","translated_internal_url":"","created_at":"2022-09-01T05:43:54.306-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":112917,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90535211,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535211/thumbnails/1.jpg","file_name":"0611064.pdf","download_url":"https://www.academia.edu/attachments/90535211/download_file","bulk_download_file_name":"Early_Greek_Thought_and_Perspectives_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535211/0611064-libre.pdf?1662037464=\u0026response-content-disposition=attachment%3B+filename%3DEarly_Greek_Thought_and_Perspectives_for.pdf\u0026Expires=1738642663\u0026Signature=ONaU5DyCE7e8bwpNE4YIx9HEKyKF8XHvH7ufTcFLqa~dCUfIBNSZ5jTcZxm3hvt7f5Qpwb--Utx3yclY~q6vtIt-T~kbn7eXxVyK~NMu296jII0ORhy3gCa5gZFQe1~5lZxGdq9bH1l3HFhKqwJfS7i~ovA1KlpjqFanZn6hMSm~hApv43Dvgj8Q7Gn8o2~2TU7oqNAPkI7QuAqDevJ9zQgz6LKUsOvSbPzp092CBrAAfhRRdEFQWMmGRM6SEOcXy2DEqSMssPI2EpmGGTU3z~PPpU0Y3XvQZ5d3hXJ3lMIvmopmnTwoEcSvGDJApo-XwJ-OZomQTVpYLPrs797yQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach","translated_slug":"","page_count":18,"language":"en","content_type":"Work","summary":"It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing \"space\" as the seat of stability, and \"time\" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.","owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535211,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535211/thumbnails/1.jpg","file_name":"0611064.pdf","download_url":"https://www.academia.edu/attachments/90535211/download_file","bulk_download_file_name":"Early_Greek_Thought_and_Perspectives_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535211/0611064-libre.pdf?1662037464=\u0026response-content-disposition=attachment%3B+filename%3DEarly_Greek_Thought_and_Perspectives_for.pdf\u0026Expires=1738642663\u0026Signature=ONaU5DyCE7e8bwpNE4YIx9HEKyKF8XHvH7ufTcFLqa~dCUfIBNSZ5jTcZxm3hvt7f5Qpwb--Utx3yclY~q6vtIt-T~kbn7eXxVyK~NMu296jII0ORhy3gCa5gZFQe1~5lZxGdq9bH1l3HFhKqwJfS7i~ovA1KlpjqFanZn6hMSm~hApv43Dvgj8Q7Gn8o2~2TU7oqNAPkI7QuAqDevJ9zQgz6LKUsOvSbPzp092CBrAAfhRRdEFQWMmGRM6SEOcXy2DEqSMssPI2EpmGGTU3z~PPpU0Y3XvQZ5d3hXJ3lMIvmopmnTwoEcSvGDJApo-XwJ-OZomQTVpYLPrs797yQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics"},{"id":12553,"name":"History of Physics","url":"https://www.academia.edu/Documents/in/History_of_Physics"},{"id":44285,"name":"Quantum Logic","url":"https://www.academia.edu/Documents/in/Quantum_Logic"},{"id":65157,"name":"Interpretation of Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Interpretation_of_Quantum_Mechanics"},{"id":123226,"name":"Classical Logic","url":"https://www.academia.edu/Documents/in/Classical_Logic"}],"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="85983352"><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/85983352/Spekkens_s_toy_theory_as_a_category_of_processes"><img alt="Research paper thumbnail of Spekkens’s toy theory as a category of processes" class="work-thumbnail" src="https://attachments.academia-assets.com/90535206/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/85983352/Spekkens_s_toy_theory_as_a_category_of_processes">Spekkens’s toy theory as a category of processes</a></div><div class="wp-workCard_item"><span>Proceedings of Symposia in Applied Mathematics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in te...</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 two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description. It is a subcategory MSpek of the category of finite sets, relations and the cartesian product. States of maximal knowledge form a subcategory Spek. This establishes the consistency of the toy theory, which has previously only been constructed for at most four systems. Our model also shows that the theory is closed under both parallel and sequential composition of operations (= symmetric monoidal structure), that it obeys map-state duality (= compact closure), and that states and effects are in bijective correspondence (= dagger structure). From the perspective of categorical quantum mechanics, this provides an interesting alternative model which enables us to describe many quantum phenomena in a discrete manner, and to which mathematical concepts such as basis structures, and complementarity thereof, still apply. Hence, the framework of categorical quantum mechanics has delivered on its promise to encompass theories other than quantum theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bd280d5988d0cc4fce44d0909043eca4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535206,"asset_id":85983352,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535206/download_file?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="85983352"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983352"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983352; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983352]").text(description); $(".js-view-count[data-work-id=85983352]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983352; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983352']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "bd280d5988d0cc4fce44d0909043eca4" } } $('.js-work-strip[data-work-id=85983352]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983352,"title":"Spekkens’s toy theory as a category of processes","internal_url":"https://www.academia.edu/85983352/Spekkens_s_toy_theory_as_a_category_of_processes","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535206,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535206/thumbnails/1.jpg","file_name":"1108.pdf","download_url":"https://www.academia.edu/attachments/90535206/download_file","bulk_download_file_name":"Spekkens_s_toy_theory_as_a_category_of_p.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535206/1108-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DSpekkens_s_toy_theory_as_a_category_of_p.pdf\u0026Expires=1740553109\u0026Signature=K9Qh7weVOPwfkiKjHQJ0Ct5wEtPPahrZ~Ai3FCZ98GWFkNpZ7BBQoZp1cvqfMiVrDPE-yBPVRKQsviz0AsRfeJHzY2TT7zKkQPwVeLSL0Z0lXPlnIyGVFJrUoYZfJBl3nGB7FeqKHuUQAvw5dLdGbPepe5dcg48cKcnFOvmAv6C3~2Tc3SW1ZKJ1EbtnIlv1Sq7NJZJDsLDsgAj9q5gppKQJI8alZr5GPWpujrE-dYvgGdkWeWaPdr5N-uqjLbSZ3nPVPSbSD43pH0HVQDGsUBuu2lG0g4QipZvg7k1BbOSVrO1U9YnIjtB5Bv5r7OY-hd0rJlmrNaeIVN4~xABqgw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983346"><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/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus"><img alt="Research paper thumbnail of Three qubit entanglement within graphical Z/X-calculus" class="work-thumbnail" src="https://attachments.academia-assets.com/90535190/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/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus">Three qubit entanglement within graphical Z/X-calculus</a></div><div class="wp-workCard_item"><span>Electronic Proceedings in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quan...</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">The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the Wand GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d742b6c25ba968d041f10149e750d3ab" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535190,"asset_id":85983346,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535190/download_file?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="85983346"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983346"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983346; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983346]").text(description); $(".js-view-count[data-work-id=85983346]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983346; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983346']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "d742b6c25ba968d041f10149e750d3ab" } } $('.js-work-strip[data-work-id=85983346]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983346,"title":"Three qubit entanglement within graphical Z/X-calculus","internal_url":"https://www.academia.edu/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535190/thumbnails/1.jpg","file_name":"1103.pdf","download_url":"https://www.academia.edu/attachments/90535190/download_file","bulk_download_file_name":"Three_qubit_entanglement_within_graphica.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535190/1103-libre.pdf?1662037465=\u0026response-content-disposition=attachment%3B+filename%3DThree_qubit_entanglement_within_graphica.pdf\u0026Expires=1740553109\u0026Signature=Kq1Zz1cPW-McHTbhYPoKVpSXwXO~5uH4NWZyyzhN6PLUCA5t4iXCe118X3QA5pPfMQxF7HqTpiBiVJIeNMHNk1L3jN9INh37KLacDbB4MppN7mj2AHsncb6TOXwpuZ5c8kEAoLeGTh6RSX-jTHmXK9SjUOCIhIyD4gb609ZX78itk4ramocUCQVDQ3YP8tDDuvadnYoRTbkRSC97o1CsmjvaAIfR-iuqHFIKfug5siT~GlVD2~JZykuNkXkExIcgz~Ajw5TsR5heCo0md~4PAYBIYmnygjf-0HVfBOBY89j~9HmWoYVKDNkMSECiNRk5VclXRciPbnwzxQ6OEVBPaw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983341"><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/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time"><img alt="Research paper thumbnail of Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time" class="work-thumbnail" src="https://attachments.academia-assets.com/90535189/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/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time">Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time</a></div><div class="wp-workCard_item"><span>Physical Review Letters</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">There is an incompatibility between the symmetries of causal structure in relativity theory and 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">There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time-reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with space-like separated input-output pairs. We explicitly describe a nonsignaling device which becomes a perfect signaling device under time-reversal, where time-reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although time-reversal of Popuscu-Rörlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time-reversal using post-selection, which could lead experimental implementation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f6eac72f55834193b76e1288e4f1ceff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535189,"asset_id":85983341,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535189/download_file?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="85983341"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983341"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983341; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983341]").text(description); $(".js-view-count[data-work-id=85983341]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983341; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983341']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "f6eac72f55834193b76e1288e4f1ceff" } } $('.js-work-strip[data-work-id=85983341]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983341,"title":"Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time","internal_url":"https://www.academia.edu/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535189,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535189/thumbnails/1.jpg","file_name":"1108.pdf","download_url":"https://www.academia.edu/attachments/90535189/download_file","bulk_download_file_name":"Time_Asymmetry_of_Probabilities_Versus_R.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535189/1108-libre.pdf?1662037463=\u0026response-content-disposition=attachment%3B+filename%3DTime_Asymmetry_of_Probabilities_Versus_R.pdf\u0026Expires=1740553109\u0026Signature=ap9NxFN5MdIg1kPjkgit46RI37CEka5h2zTBsHKU7QzmN0Ii3g7K1Ch4hQWjUjEWWSbtUeB8~tBL6g1XomjHiOqpR3afKkrimr6eVXPbuaMPryQXfQsgKOsd7w2KZF5WzWb1FuNEKDbeEpOxja5yITn9ctdODGGVKSb3WBq2rzmtkeDybwTSKcOaGh8Tfw-i6QTOpdsUiQykTUVd1yYwqZ9ner6Hbq7RaDLJTJGRrikim8wGZw5ORH~G5qd2q~ulziKukaSpIO9rn6KlZoOGcA~Fnx0WlVVD6-khyr99m~bDeFeEAriGDLIa6iqvR60MJkY0RxBSzcxbgYbTl3hFyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983337"><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/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics"><img alt="Research paper thumbnail of Interacting quantum observables: categorical algebra and diagrammatics" class="work-thumbnail" src="https://attachments.academia-assets.com/90535188/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/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics">Interacting quantum observables: categorical algebra and diagrammatics</a></div><div class="wp-workCard_item"><span>New Journal of Physics</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphica...</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 paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the zx-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z and X spin observables, which yields a scaled variant of a bialgebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4a6bdfb47f73d5aea5364bb4295be582" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535188,"asset_id":85983337,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535188/download_file?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="85983337"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983337"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983337; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983337]").text(description); $(".js-view-count[data-work-id=85983337]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983337; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983337']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "4a6bdfb47f73d5aea5364bb4295be582" } } $('.js-work-strip[data-work-id=85983337]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983337,"title":"Interacting quantum observables: categorical algebra and diagrammatics","internal_url":"https://www.academia.edu/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535188/thumbnails/1.jpg","file_name":"0906.pdf","download_url":"https://www.academia.edu/attachments/90535188/download_file","bulk_download_file_name":"Interacting_quantum_observables_categori.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535188/0906-libre.pdf?1662037508=\u0026response-content-disposition=attachment%3B+filename%3DInteracting_quantum_observables_categori.pdf\u0026Expires=1740553109\u0026Signature=GRu5k5kFRy2E8-gXJwXMpnej9Z8ev8htAnQU3SLKDa3RRYul9cSpHQIsfH8B5tZEZND4IaKujZ3Uiet34FGaiOhLXwBpChUGhC6SrEY5ywOpswDZPhGYI3aZBCwS2hXRO90InZNqY9sp8ko3J7cuMAWX3vcSHfmazXuMkrLxOSTlc6buGLd-1VIfDsg9fWbJMoh5WRawzosBbx1vmtt0X-pV8stNUIOUpZEqrikK5BWwYeHOVg9SO5SIXLTVFdxSyaJ0DA3cXZ6YeHGsBuewuNnAnHKprjC1eCelTCvh-Tx5g9PMl1jz8lWXy4vLwQncMStnI68aE3R10RDwfarEwA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983327"><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/85983327/Causal_Categories_Relativistically_Interacting_Processes"><img alt="Research paper thumbnail of Causal Categories: Relativistically Interacting Processes" class="work-thumbnail" src="https://attachments.academia-assets.com/90535181/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/85983327/Causal_Categories_Relativistically_Interacting_Processes">Causal Categories: Relativistically Interacting Processes</a></div><div class="wp-workCard_item"><span>Foundations of Physics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A symmetric monoidal category naturally arises as the mathematical structure that organizes physi...</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">A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4c3f84eb76f5f69472ad3900626cf28e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535181,"asset_id":85983327,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535181/download_file?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="85983327"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983327"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983327; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983327]").text(description); $(".js-view-count[data-work-id=85983327]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983327; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983327']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "4c3f84eb76f5f69472ad3900626cf28e" } } $('.js-work-strip[data-work-id=85983327]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983327,"title":"Causal Categories: Relativistically Interacting Processes","internal_url":"https://www.academia.edu/85983327/Causal_Categories_Relativistically_Interacting_Processes","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535181,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535181/thumbnails/1.jpg","file_name":"1107.pdf","download_url":"https://www.academia.edu/attachments/90535181/download_file","bulk_download_file_name":"Causal_Categories_Relativistically_Inter.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535181/1107-libre.pdf?1662037476=\u0026response-content-disposition=attachment%3B+filename%3DCausal_Categories_Relativistically_Inter.pdf\u0026Expires=1740553109\u0026Signature=Ee6RaCiX5IbqO3iYpb3HnKCsIxByx~gSE1P2oSps9cbblZuuzftODeK5Chm4w7HMXtyn3pXVi0woDAVAjEmUDXPzyavuwDo8oKG47ZgKQWApeXu4SsgGyIydazitDznzvGBNu~JEedw3gosiT~SNsbuyHWgk6rUItOisnbg5UOS3r86~j6gQmZ6zMGcsjxCHPGK8vWLUPmdCdwRpnG4q96xtsvx0fmXX~mOqH1o5DR~-c2ff3j1lC5OrGSNlbVOylSev5ogQyqQGNhY6cOQIaTUgt9yD4XWvFY5gR1nw59LAWyVl7YMlAVby7dxvJluXGLy7OYQ-B-eL1oXb72qu1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983320"><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/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_"><img alt="Research paper thumbnail of Graphical Calculus for Quantum Key Distribution (Extended Abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/90535171/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/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_">Graphical Calculus for Quantum Key Distribution (Extended Abstract)</a></div><div class="wp-workCard_item"><span>Electronic Notes in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Controlled complementary measurements are key to quantum key distribution protocols, among many 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">Controlled complementary measurements are key to quantum key distribution protocols, among many other things. We axiomatize controlled complementary measurements within symmetric monoidal categories, which provides them with a corresponding graphical calculus. We study the BB84 and Ekert91 protocols within this calculus, including the case where there is an intercept-resend attack.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a5909da1d21aca4d6ccfcac07e32b32f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535171,"asset_id":85983320,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535171/download_file?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="85983320"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983320"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983320; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983320]").text(description); $(".js-view-count[data-work-id=85983320]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983320; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983320']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "a5909da1d21aca4d6ccfcac07e32b32f" } } $('.js-work-strip[data-work-id=85983320]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983320,"title":"Graphical Calculus for Quantum Key Distribution (Extended Abstract)","internal_url":"https://www.academia.edu/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535171,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535171/thumbnails/1.jpg","file_name":"82074856.pdf","download_url":"https://www.academia.edu/attachments/90535171/download_file","bulk_download_file_name":"Graphical_Calculus_for_Quantum_Key_Distr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535171/82074856-libre.pdf?1662037472=\u0026response-content-disposition=attachment%3B+filename%3DGraphical_Calculus_for_Quantum_Key_Distr.pdf\u0026Expires=1740553109\u0026Signature=UK8-APUr9d4EUm7v145j-mesSC4x0QWfcdpheCwbcHOD8f2VXra1qsGpxZ89ZDM~iYR~FG-Y032HeMjjgSZ1g13np8CLg9OkgdkFmFe4Tmu1V1qBxgpqkfmrGd5rgCsp0Tw~H4ycdBHu4VE5PLI~dYLRHHBlPvr5vhiwOpJJkYGtxSDYY2-u6PNIFQlTDZCnFmWBBLT~Eon8zjXSc1yx7-y49x4i2c6PaPEPEN6FeUh3C4jGNlDp9N83wAGBems0TuEQHeEt4bPU64jLuzxR9cqSJrLaErZNic-iSM39tK2OA3sGEqpILPwZWViYBYATPz7owFPYrzzX4rMRXwOy5w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983313"><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/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning"><img alt="Research paper thumbnail of Towards a Compositional Distributional Model of Meaning" class="work-thumbnail" src="https://attachments.academia-assets.com/90535160/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/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning">Towards a Compositional Distributional Model of Meaning</a></div><div class="wp-workCard_item"><span>comlab.ox.ac.uk</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We propose a mathematical framework for a unifica-tion of the distributional theory of meaning in...</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 propose a mathematical framework for a unifica-tion of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, namely Lambek&#x27;s pregroup seman-tics. A key observation is that the monoidal category of (finite ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="edc347ee114b0280ef13fe1fda806c9f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535160,"asset_id":85983313,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535160/download_file?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="85983313"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983313"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983313; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983313]").text(description); $(".js-view-count[data-work-id=85983313]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983313; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983313']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "edc347ee114b0280ef13fe1fda806c9f" } } $('.js-work-strip[data-work-id=85983313]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983313,"title":"Towards a Compositional Distributional Model of Meaning","internal_url":"https://www.academia.edu/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535160/thumbnails/1.jpg","file_name":"AAAI_2008.pdf","download_url":"https://www.academia.edu/attachments/90535160/download_file","bulk_download_file_name":"Towards_a_Compositional_Distributional_M.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535160/AAAI_2008-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DTowards_a_Compositional_Distributional_M.pdf\u0026Expires=1740553109\u0026Signature=RiovyLzD0N3uE2ym3oGlKlqG49V2mp~yd55MoQ0arRAIllIhFH-TfbJTMqx0E0bzD5P1Ilw3mqocVbqE2XbwyATVsPjpqIwDfKoK94BfeX~JcuX69ZEATj3QLsx2f5VUS-fvi62sk~3YvzSrMFlTnyKWyiRcy7bCrpAt0PcfH8jbI52fU~07yXlwoC8uQE1VjxEQ10SsxvYPjSDSHdhCznumhxAPn3SZCR-pW83qshpvl5X6L0jiXgiLiTV1dyCr5x8FQ2ufsCVIrQAJMTM7mIkDeK~K2VZggYNw1cpDpMSwEyDo1N~ooNSvQIRtydqeSZoI1oBNZKMhZMcFAGYhog__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983306"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_"><img alt="Research paper thumbnail of Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_">Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)</a></div><div class="wp-workCard_item"><span>atlas-conferences.com</span><span>, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLAS...</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">Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL&#x27;07) August 5-9, 2007 St Anne&#x27;s College, University of Oxford Oxford, England. Organizers Mai Gehrke and Hilary Priestley. Conference Homepage. Abstracts. SAMSON ABRAMSKY Domain Theory in Logical Form Revisited: a 20-year Retrospective Stefano Aguzzoli Goedel algebras free over finite distributive ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="85983306"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983306"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983306; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983306]").text(description); $(".js-view-count[data-work-id=85983306]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983306; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983306']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=85983306]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983306,"title":"Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)","internal_url":"https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="85983300"><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/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences"><img alt="Research paper thumbnail of Diagrammatic Reasoning about Meaning of Sentences" class="work-thumbnail" src="https://attachments.academia-assets.com/90535147/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/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences">Diagrammatic Reasoning about Meaning of Sentences</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The symbolic [5] and distributional [8] theories of meaning are somewhat orthogonal with competin...</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">The symbolic [5] and distributional [8] theories of meaning are somewhat orthogonal with competing pros and cons: the former is compositional but only qualitative, the latter is non-compositional but quantitative. Following [9] in the context of Cognitive Science, where a similar problem exists between the connectionist and symbolic models of mind,[3] argued for the use of the tensor product of vector spaces and pairing the vectors of meaning with their syntactic roles. This abstract summarizes the framework developed in [2], which builds on ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="aa2d1af71b2d470fd0598d3b31d8001e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535147,"asset_id":85983300,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535147/download_file?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="85983300"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983300"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983300; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983300]").text(description); $(".js-view-count[data-work-id=85983300]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983300; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983300']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "aa2d1af71b2d470fd0598d3b31d8001e" } } $('.js-work-strip[data-work-id=85983300]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983300,"title":"Diagrammatic Reasoning about Meaning of Sentences","internal_url":"https://www.academia.edu/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535147,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535147/thumbnails/1.jpg","file_name":"distcomp2010_clark_etal_9.pdf","download_url":"https://www.academia.edu/attachments/90535147/download_file","bulk_download_file_name":"Diagrammatic_Reasoning_about_Meaning_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535147/distcomp2010_clark_etal_9-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DDiagrammatic_Reasoning_about_Meaning_of.pdf\u0026Expires=1740553109\u0026Signature=SzSMzFPu8PQ~lFLDAuwZiYqzKqPdsVvvSHvG05~NO7gsDzYeRZUsgTecT-HizEJ9VR6vk-uimpxdAo1X4tS3HiU2ZElV34Fjsx82eiddMRt5JGH3eX9zpE2tJKgjxf2X1i9-wj-fLovOn1UttZkouFaY69mjL6WjmxqJG0eleYrs-c9Yay0E~8wGNcS3i7bA1xFXEOCrmE~LR1rZcel0kfGzED-KxgxK0iIB83qQaNgtIXH~GIKXblVWdPHw9FOfa8095oqZqV4CXMTkxYMw5HRYxEBjjS-ERpN3dHrepBlzVFYIvn5olU-htlesh9nQ50hNaKq2zWy3xwOiSqXtnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983296"><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/85983296/Partiality_in_physics"><img alt="Research paper thumbnail of Partiality in physics" class="work-thumbnail" src="https://attachments.academia-assets.com/90535140/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/85983296/Partiality_in_physics">Partiality in physics</a></div><div class="wp-workCard_item"><span>arXiv preprint quant-ph/0312044</span><span>, Dec 4, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Abstract: We revisit the standard axioms of domain theory with emphasis on their relation to the ...</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">Abstract: We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting capable of providing a satisfactory unification of the two.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0c993d8f1734040b9fd6f263c3683063" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535140,"asset_id":85983296,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535140/download_file?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="85983296"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983296"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983296; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983296]").text(description); $(".js-view-count[data-work-id=85983296]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983296; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983296']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "0c993d8f1734040b9fd6f263c3683063" } } $('.js-work-strip[data-work-id=85983296]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983296,"title":"Partiality in physics","internal_url":"https://www.academia.edu/85983296/Partiality_in_physics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535140,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535140/thumbnails/1.jpg","file_name":"0312044.pdf","download_url":"https://www.academia.edu/attachments/90535140/download_file","bulk_download_file_name":"Partiality_in_physics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535140/0312044-libre.pdf?1662037478=\u0026response-content-disposition=attachment%3B+filename%3DPartiality_in_physics.pdf\u0026Expires=1740553109\u0026Signature=aQ5W2u5x81QfLkySnWWJHTFkBKfBTNe8WXjfNVtg7lin0-Rb7tr324PJ8AGJRBJJGzc2z~Yw8MzyTB-Gel20dSaVUImfcKF4v3tg48dagKiziarFnJ6EkHRxLZ9gSNi53ogwRirvinZRQ1PmQHNjAWHRxqGfOwUg4PtYo2~LFjUHCJkEluk4AdhqzsCkRRbaPa2a8Nbn~08OhVmhxofwsoHwlP8l~3D86ss8gBbA4eHOAPrq54uRhavUo3ejjSsHw1ilXMhKoV7V3iTY~ym-TQpkdk4d6bFqiHJdRn9ULoixXRNRfJ3U8LZfAoRz0~ovNEvOhZaHyTKZhnlGWXkPXw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983232"><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/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras"><img alt="Research paper thumbnail of Reasoning about meaning in natural language with compact closed categories and Frobenius algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/90535104/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/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras">Reasoning about meaning in natural language with compact closed categories and Frobenius algebras</a></div><div class="wp-workCard_item"><span>Logic and Algebraic Structures in Quantum Computing</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Compact closed categories have found applications in modeling quantum information protocols by Ab...</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">Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural language, and are implicit in a distributional model of word meaning based on vector spaces. Specifically, in previous work Coecke-Clark-Sadrzadeh used the product category of pregroups with vector spaces and provided a distributional model of meaning for sentences. We recast this theory in terms of strongly monoidal functors and advance it via Frobenius algebras over vector spaces. The former are used to formalize topological quantum field theories by Atiyah and Baez-Dolan, and the latter are used to model classical data in quantum protocols by Coecke-Pavlovic-Vicary. The Frobenius algebras enable us to work in a single space in which meanings of words, phrases, and sentences of any structure live. Hence we can compare meanings of different language constructs and enhance the applicability of the theory. We report on experimental results on a number of language tasks and verify the theoretical predictions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fb20aeb0d7210d01a63058ff4e19458a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535104,"asset_id":85983232,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535104/download_file?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="85983232"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983232"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983232; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983232]").text(description); $(".js-view-count[data-work-id=85983232]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983232; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983232']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "fb20aeb0d7210d01a63058ff4e19458a" } } $('.js-work-strip[data-work-id=85983232]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983232,"title":"Reasoning about meaning in natural language with compact closed categories and Frobenius algebras","internal_url":"https://www.academia.edu/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535104,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535104/thumbnails/1.jpg","file_name":"1401.5980.pdf","download_url":"https://www.academia.edu/attachments/90535104/download_file","bulk_download_file_name":"Reasoning_about_meaning_in_natural_langu.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535104/1401.5980-libre.pdf?1662037482=\u0026response-content-disposition=attachment%3B+filename%3DReasoning_about_meaning_in_natural_langu.pdf\u0026Expires=1740553109\u0026Signature=JBiGX5rnNwSiOqLcCbvt5exBsub9-MgkiaobafnIjnUQtaj7fIFcMJCTgv-3MMqhOSMHmVdfk9qELoDA4OP~jEVL3sO1lbO-unJXHgAliCfl1Rkw03PMv-ux~K9-GmY1ydCpk~i0GFogI7bqAP7U24yx62mhIdOywN7Qcy7GaOmVS7sqPRgx7y0wvek9rMJtchP-cKC4f7ZamStg0nmy9tsiaNS-oma~-uM1kAVIx4XG6f4JdrLkSkm0SHMXbFwr2VqWiXPQ9ljAtLIv1LKmgc9a~Ikd9nMqGlC8rzhz7Mls-y4HR4-ECHLD~h0dw310t2ZL0rpM06Oav0wdWJ5erw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="80860334"><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/80860334/Toy_Quantum_Categories_Extended_Abstract_"><img alt="Research paper thumbnail of Toy Quantum Categories (Extended Abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/87101250/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/80860334/Toy_Quantum_Categories_Extended_Abstract_">Toy Quantum Categories (Extended Abstract)</a></div><div class="wp-workCard_item"><span>Electronic Notes in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach 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 that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set in FRel.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="add920fcde17596377a6c31c1168715a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87101250,"asset_id":80860334,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87101250/download_file?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="80860334"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80860334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80860334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=80860334]").text(description); $(".js-view-count[data-work-id=80860334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 80860334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='80860334']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "add920fcde17596377a6c31c1168715a" } } $('.js-work-strip[data-work-id=80860334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":80860334,"title":"Toy Quantum Categories (Extended Abstract)","internal_url":"https://www.academia.edu/80860334/Toy_Quantum_Categories_Extended_Abstract_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":87101250,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/87101250/thumbnails/1.jpg","file_name":"82443403.pdf","download_url":"https://www.academia.edu/attachments/87101250/download_file","bulk_download_file_name":"Toy_Quantum_Categories_Extended_Abstract.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/87101250/82443403-libre.pdf?1654548069=\u0026response-content-disposition=attachment%3B+filename%3DToy_Quantum_Categories_Extended_Abstract.pdf\u0026Expires=1740553109\u0026Signature=VkipwGOFuIEjj13zD0jb76VBWAVvvN3By6iGQewMFu61eWhtKx-mBlG6owYE6KKShOEzJDdTGRanM0mZXOEvLKvryap9JY6Hsf4yGvX0IsHPvZ6ZCza4e3dQPoYr~PKhomKbDVG5YS77CMWuaPJ44hpXipLrdpKbJBIb4hBRQHa~Q8~aIDhquO9ekT9SpjFOMQGdLVzk4z9wESfNwgu35zL20MKD~4CJXBWKeOsfWmDp4Jml~NqMW6M1pHk7pl2GZ8ddn3F7Nj-4Wu5WgrQtJ-v~SI7qray8bmGi92KJ6U08QjeHS1aIZjnfUI6G7lLPCGIXbuBMu7sDzbXYSzcXnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="11853" id="papers"><div class="js-work-strip profile--work_container" data-work-id="94621890"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift"><img alt="Research paper thumbnail of Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift">Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift</a></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="94621890"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621890"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621890; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621890]").text(description); $(".js-view-count[data-work-id=94621890]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621890; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621890']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621890]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621890,"title":"Mathematical Foundations for Distributed Compositional Model of Meaning. Lambek Festschrift","internal_url":"https://www.academia.edu/94621890/Mathematical_Foundations_for_Distributed_Compositional_Model_of_Meaning_Lambek_Festschrift","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621889"><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/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits"><img alt="Research paper thumbnail of Tutorial: Graphical Calculus for Quantum Circuits" class="work-thumbnail" src="https://attachments.academia-assets.com/97028021/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/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits">Tutorial: Graphical Calculus for Quantum Circuits</a></div><div class="wp-workCard_item"><span>Reversible Computation</span><span>, 2013</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We explain the graphical zx-calculus for reasoning about qubits without any reference to the unde...</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 explain the graphical zx-calculus for reasoning about qubits without any reference to the underlying categorical semantics, and illustrate its use on quantum circuits.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f37695b86b4d1897c363fc45e52ad3d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97028021,"asset_id":94621889,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97028021/download_file?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="94621889"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621889"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621889; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621889]").text(description); $(".js-view-count[data-work-id=94621889]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621889; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621889']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "9f37695b86b4d1897c363fc45e52ad3d" } } $('.js-work-strip[data-work-id=94621889]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621889,"title":"Tutorial: Graphical Calculus for Quantum Circuits","internal_url":"https://www.academia.edu/94621889/Tutorial_Graphical_Calculus_for_Quantum_Circuits","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97028021,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97028021/thumbnails/1.jpg","file_name":"978-3-642-36315-3_1.pdf","download_url":"https://www.academia.edu/attachments/97028021/download_file","bulk_download_file_name":"Tutorial_Graphical_Calculus_for_Quantum.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97028021/978-3-642-36315-3_1-libre.pdf?1673266130=\u0026response-content-disposition=attachment%3B+filename%3DTutorial_Graphical_Calculus_for_Quantum.pdf\u0026Expires=1740553109\u0026Signature=Qz27gVaMKpjQUwX3LplHcQ8sTJQyBW32MAalIJYnplZx5zyEJbjZ-f-heFwq8qy4kU64wrC1xviQGdq2lrmXWNzwjqH2Sd9WZfKAMonCNUGNwwDBGeVnDvNbUJBu~u53qgWU7Ox4BxLbFFs6LSi0Vtju~5vJjnHJsMai25yKluZBwIjl3h-FfQGfgdhI~n36A7EJHn1iqA3ON-0Uh-6ba7lVSmIrIK7spUV3kYGQqcbCodIYS40N9Yy22dOMClbKzC2lShh7alxdMAxD62r95r47RW9GctmG-1Oc2EAkCOIRwwS0E~amrY0ymMvn4KyLylnt3QxsuAccxiYyAujVWg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="94621888"><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/94621888/Partiality_in_physics"><img alt="Research paper thumbnail of Partiality in physics" class="work-thumbnail" src="https://attachments.academia-assets.com/97028004/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/94621888/Partiality_in_physics">Partiality in physics</a></div><div class="wp-workCard_item"><span>Computing Research Repository - CORR</span><span>, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We revisit the standard axioms of domain theory with emphasis on their relation to the concept of...</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 revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting capable of providing a satisfactory unification of the two. finite string is partial, the infinite strings are total. In the domain (IR, ⊑), the collection of compact intervals (a, b) of the real line ordered by reverse inclusion, an interval like (p, q) with p &lt; q rational is partial, while a one point interval (x) representing a real number is total. In the domain (n, ⊑), the n dimensional mixed states in the spectral order (to be defined later), a pure state is total, while mixed states which are not pure are partial. In all the cases above, total elements coincide with elements which are maximal in the given order. As we can see, the partiality idea arises naturally in both computer science and physics. The idea is important in computer scienc...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="70e1b47d269510b013da78da9729ae08" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97028004,"asset_id":94621888,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97028004/download_file?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="94621888"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621888"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621888; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621888]").text(description); $(".js-view-count[data-work-id=94621888]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621888; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621888']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "70e1b47d269510b013da78da9729ae08" } } $('.js-work-strip[data-work-id=94621888]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621888,"title":"Partiality in physics","internal_url":"https://www.academia.edu/94621888/Partiality_in_physics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97028004,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97028004/thumbnails/1.jpg","file_name":"0312044v1.pdf","download_url":"https://www.academia.edu/attachments/97028004/download_file","bulk_download_file_name":"Partiality_in_physics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97028004/0312044v1-libre.pdf?1673266136=\u0026response-content-disposition=attachment%3B+filename%3DPartiality_in_physics.pdf\u0026Expires=1740553109\u0026Signature=fw2o1lVB4hxni3XkKzWLzkrC3F0y-7iKlbv4XLoETieKwFankrvpM7D0apN6twGWsJ5YAuWnbRh65UFnlLGzoLoklLFAlQuA4mYi~s7Low0jvWkhZj1KLUpLVWxCl9og8Q79r-VbiDn649KMSYHMyzQE0WaFUGj1~ZyMlt14QZAhwff~JzmTXHgcxm5WESZ3L0Jvi9r7AxK0o1H9wK7xdWNC2MkrAyVyZ9vUf61MQiIqySXO5jP6HPA~jX7ZYkEPXST3H77wlyG9zNZwF0tY4mcrctEWzNavLG2G9Sd3jqUyYq~zW37MYvPUT1d52RGONJe5YAhD2fv5O8jU2QH5sg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="94621887"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics"><img alt="Research paper thumbnail of Domain theory and quantum mechanics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics">Domain theory and quantum mechanics</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce a partial order on classical and quantum states which reveals that these sets are ac...</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 introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same way that the order on a domain provides a rigorous qualitative definition of information, a special type of mapping on a domain called a measurement provides a formal account of ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="94621887"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621887"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621887; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621887]").text(description); $(".js-view-count[data-work-id=94621887]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621887; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621887']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621887]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621887,"title":"Domain theory and quantum mechanics","internal_url":"https://www.academia.edu/94621887/Domain_theory_and_quantum_mechanics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621886"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_"><img alt="Research paper thumbnail of Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_">Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)</a></div><div class="wp-workCard_item"><span>QPL 2011</span><span>, Oct 27, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This position paper serves two purposes:(1) In the light of recent reconstructions of quantum the...</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 position paper serves two purposes:(1) In the light of recent reconstructions of quantum theory, this paper shows the need for a representation theorem for categorical quantum mechanics (CQM), which establishes how conceptually-meaningful constructions on processes and their compositions lead to Hilbert space structure, without any reference of instrumentalist concepts such as measurement.(2) As a first step towards this goal we show how several of the instrumentalist principles underpinning Pavia&#x27;s reconstruction of finitary ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="94621886"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621886"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621886; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621886]").text(description); $(".js-view-count[data-work-id=94621886]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621886; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621886']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=94621886]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621886,"title":"Categorical quantum mechanics meets the Pavia principles: towards a representation theorem for CQM constructions (position paper)","internal_url":"https://www.academia.edu/94621886/Categorical_quantum_mechanics_meets_the_Pavia_principles_towards_a_representation_theorem_for_CQM_constructions_position_paper_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="94621885"><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/94621885/Toy_quantum_categories"><img alt="Research paper thumbnail of Toy quantum categories" class="work-thumbnail" src="https://attachments.academia-assets.com/97027924/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/94621885/Toy_quantum_categories">Toy quantum categories</a></div><div class="wp-workCard_item"><span>Electronic notes in theoretical computer science</span><span>, Feb 10, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that Rob Spekken&#x27;s toy quantum theory arises as an instance of our categorical appro...</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 that Rob Spekken&#x27;s toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="450a93f09f2b62055b45465b46113ee9" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":97027924,"asset_id":94621885,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/97027924/download_file?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="94621885"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="94621885"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 94621885; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=94621885]").text(description); $(".js-view-count[data-work-id=94621885]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 94621885; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='94621885']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "450a93f09f2b62055b45465b46113ee9" } } $('.js-work-strip[data-work-id=94621885]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":94621885,"title":"Toy quantum categories","internal_url":"https://www.academia.edu/94621885/Toy_quantum_categories","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":97027924,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/97027924/thumbnails/1.jpg","file_name":"0808.pdf","download_url":"https://www.academia.edu/attachments/97027924/download_file","bulk_download_file_name":"Toy_quantum_categories.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/97027924/0808-libre.pdf?1673266138=\u0026response-content-disposition=attachment%3B+filename%3DToy_quantum_categories.pdf\u0026Expires=1740553109\u0026Signature=Yq8un8yRz1O8uJ2Is6Av1YO2pdgw3rN~W54-36P851OyUciXvpqPUbXp0if1DkVDC6IFHvazf48zjeXIUd7IvL6Rk5MtECULCa-R-MuR0DLUG6eeIhHJ0paJi-RfIoUHZWAGw0Tz34-v~q4rXmQKUqSk4wwxt6aNoxCcnj8XocP2lIvaZGc4qoulD4YQ5muRb50bA6y7ydX4tp0NShZLZYbBuQiltDAuO0eKilmCJJHnNhO-Y5mG8urSaqJ1O2rPMz6zLku0EWMN3PKnnPNgj-5b25U30Ygpsj9nwErseFqdlJo5X2ULnaxs~xsg5R-B4x1vI631J3L8iz0w7huvtg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983362"><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/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement"><img alt="Research paper thumbnail of The Compositional Structure of Multipartite Quantum Entanglement" class="work-thumbnail" src="https://attachments.academia-assets.com/90535223/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/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement">The Compositional Structure of Multipartite Quantum Entanglement</a></div><div class="wp-workCard_item"><span>Automata, Languages and Programming</span><span>, 2010</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">While multipartite quantum states constitute a (if not the) key resource for quantum computations...</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">While multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols, obtaining a high-level, structural understanding of entanglement involving arbitrarily many qubits is a longstanding open problem in quantum computer science. In this paper we expose the algebraic and graphical structure of the GHZ-state and the W-state, as well as a purely graphical distinction that characterises the behaviours of these states. In turn, this structure yields a compositional graphical model for expressing general multipartite states. We identify those states, named Frobenius states, which canonically induce an algebraic structure, namely the structure of a commutative Frobenius algebra (CFA). We show that all SLOCC-maximal tripartite qubit states are locally equivalent to Frobenius states. Those that are SLOCC-equivalent to the GHZ-state induce special commutative Frobenius algebras, while those that are SLOCC-equivalent to the W-state induce what we call anti-special commutative Frobenius algebras. From the SLOCC-classification of tripartite qubit states follows a representation theorem for two dimensional CFAs. Together, a GHZ and a W Frobenius state form the primitives of a graphical calculus. This calculus is expressive enough to generate and reason about arbitrary multipartite states, which are obtained by "composing" the GHZ-and W-states, giving rise to a rich graphical paradigm for general multipartite entanglement.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="7d1de0961e86dc0300e243e6ee62f59a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535223,"asset_id":85983362,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535223/download_file?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="85983362"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983362"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983362; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983362]").text(description); $(".js-view-count[data-work-id=85983362]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983362; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983362']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "7d1de0961e86dc0300e243e6ee62f59a" } } $('.js-work-strip[data-work-id=85983362]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983362,"title":"The Compositional Structure of Multipartite Quantum Entanglement","internal_url":"https://www.academia.edu/85983362/The_Compositional_Structure_of_Multipartite_Quantum_Entanglement","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535223,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535223/thumbnails/1.jpg","file_name":"1002.pdf","download_url":"https://www.academia.edu/attachments/90535223/download_file","bulk_download_file_name":"The_Compositional_Structure_of_Multipart.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535223/1002-libre.pdf?1662037467=\u0026response-content-disposition=attachment%3B+filename%3DThe_Compositional_Structure_of_Multipart.pdf\u0026Expires=1740553109\u0026Signature=TXEh6FX8BP8~l9X6bDYWW-9kcBSP6nLmWHL677eMNBiMfaSKfP-xCaRneUe1QNo-JDOn9ggWOI9v-4gTU6~OER9EE~ZpunxoR5ZtFqahncMbQBxzpHKZJuC~a~YJMCXZ-XFkG-pvFzuDYwMZarl~L-i1bLxeJTuqtMKgWYcgDlZPhEwY5Q0Jy61SkQ0~E1qWa98ZXNU3vft65qK4fRmkUwS6R~ud8BDECu~sOmdXJ~PRhhHD1jsMz5I8Idcz5bMYpiQKZk4aI1rQY1zwhjlvy62jk6TJZjoKzrQ9JBHRhq7x9Wwz4OaDw7IiEHsam-3VJM9g3QWk8IOz93J2h-i2kw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983356"><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/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach"><img alt="Research paper thumbnail of Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach" class="work-thumbnail" src="https://attachments.academia-assets.com/90535211/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/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach">Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach</a></div><div class="wp-workCard_item"><span>Metadebates on Science</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">It will be shown in this article that an ontological approach for some problems related to the in...</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">It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing "space" as the seat of stability, and "time" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="1ebb2a49fdb3ccc1021fce5c10b273cf" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535211,"asset_id":85983356,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535211/download_file?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="85983356"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983356"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983356; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983356]").text(description); $(".js-view-count[data-work-id=85983356]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983356; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983356']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "1ebb2a49fdb3ccc1021fce5c10b273cf" } } $('.js-work-strip[data-work-id=85983356]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983356,"title":"Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach","translated_title":"","metadata":{"grobid_abstract":"It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing \"space\" as the seat of stability, and \"time\" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Metadebates on Science","grobid_abstract_attachment_id":90535211},"translated_abstract":null,"internal_url":"https://www.academia.edu/85983356/Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach","translated_internal_url":"","created_at":"2022-09-01T05:43:54.306-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":112917,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":90535211,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535211/thumbnails/1.jpg","file_name":"0611064.pdf","download_url":"https://www.academia.edu/attachments/90535211/download_file","bulk_download_file_name":"Early_Greek_Thought_and_Perspectives_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535211/0611064-libre.pdf?1662037464=\u0026response-content-disposition=attachment%3B+filename%3DEarly_Greek_Thought_and_Perspectives_for.pdf\u0026Expires=1738642663\u0026Signature=ONaU5DyCE7e8bwpNE4YIx9HEKyKF8XHvH7ufTcFLqa~dCUfIBNSZ5jTcZxm3hvt7f5Qpwb--Utx3yclY~q6vtIt-T~kbn7eXxVyK~NMu296jII0ORhy3gCa5gZFQe1~5lZxGdq9bH1l3HFhKqwJfS7i~ovA1KlpjqFanZn6hMSm~hApv43Dvgj8Q7Gn8o2~2TU7oqNAPkI7QuAqDevJ9zQgz6LKUsOvSbPzp092CBrAAfhRRdEFQWMmGRM6SEOcXy2DEqSMssPI2EpmGGTU3z~PPpU0Y3XvQZ5d3hXJ3lMIvmopmnTwoEcSvGDJApo-XwJ-OZomQTVpYLPrs797yQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Early_Greek_Thought_and_Perspectives_for_the_Interpretation_of_Quantum_Mechanics_Preliminaries_to_an_Ontological_Approach","translated_slug":"","page_count":18,"language":"en","content_type":"Work","summary":"It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the coincidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato's Theory of Forms and Aristotle's metaphysics and logic. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a 'principle of contradiction' is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing \"space\" as the seat of stability, and \"time\" as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion 'separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of 'non-locality' as related to it, indicating the need to rethink the notions system, entity, as well as the implications of the operation 'measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world. 54 Here, 'induction' does not refer to any of its usual philosophical significances, but rather refers to physical theories like electro-magnetism.","owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535211,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535211/thumbnails/1.jpg","file_name":"0611064.pdf","download_url":"https://www.academia.edu/attachments/90535211/download_file","bulk_download_file_name":"Early_Greek_Thought_and_Perspectives_for.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535211/0611064-libre.pdf?1662037464=\u0026response-content-disposition=attachment%3B+filename%3DEarly_Greek_Thought_and_Perspectives_for.pdf\u0026Expires=1738642663\u0026Signature=ONaU5DyCE7e8bwpNE4YIx9HEKyKF8XHvH7ufTcFLqa~dCUfIBNSZ5jTcZxm3hvt7f5Qpwb--Utx3yclY~q6vtIt-T~kbn7eXxVyK~NMu296jII0ORhy3gCa5gZFQe1~5lZxGdq9bH1l3HFhKqwJfS7i~ovA1KlpjqFanZn6hMSm~hApv43Dvgj8Q7Gn8o2~2TU7oqNAPkI7QuAqDevJ9zQgz6LKUsOvSbPzp092CBrAAfhRRdEFQWMmGRM6SEOcXy2DEqSMssPI2EpmGGTU3z~PPpU0Y3XvQZ5d3hXJ3lMIvmopmnTwoEcSvGDJApo-XwJ-OZomQTVpYLPrs797yQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics"},{"id":12553,"name":"History of Physics","url":"https://www.academia.edu/Documents/in/History_of_Physics"},{"id":44285,"name":"Quantum Logic","url":"https://www.academia.edu/Documents/in/Quantum_Logic"},{"id":65157,"name":"Interpretation of Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Interpretation_of_Quantum_Mechanics"},{"id":123226,"name":"Classical Logic","url":"https://www.academia.edu/Documents/in/Classical_Logic"}],"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="85983352"><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/85983352/Spekkens_s_toy_theory_as_a_category_of_processes"><img alt="Research paper thumbnail of Spekkens’s toy theory as a category of processes" class="work-thumbnail" src="https://attachments.academia-assets.com/90535206/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/85983352/Spekkens_s_toy_theory_as_a_category_of_processes">Spekkens’s toy theory as a category of processes</a></div><div class="wp-workCard_item"><span>Proceedings of Symposia in Applied Mathematics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in te...</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 two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description. It is a subcategory MSpek of the category of finite sets, relations and the cartesian product. States of maximal knowledge form a subcategory Spek. This establishes the consistency of the toy theory, which has previously only been constructed for at most four systems. Our model also shows that the theory is closed under both parallel and sequential composition of operations (= symmetric monoidal structure), that it obeys map-state duality (= compact closure), and that states and effects are in bijective correspondence (= dagger structure). From the perspective of categorical quantum mechanics, this provides an interesting alternative model which enables us to describe many quantum phenomena in a discrete manner, and to which mathematical concepts such as basis structures, and complementarity thereof, still apply. Hence, the framework of categorical quantum mechanics has delivered on its promise to encompass theories other than quantum theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="bd280d5988d0cc4fce44d0909043eca4" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535206,"asset_id":85983352,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535206/download_file?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="85983352"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983352"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983352; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983352]").text(description); $(".js-view-count[data-work-id=85983352]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983352; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983352']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "bd280d5988d0cc4fce44d0909043eca4" } } $('.js-work-strip[data-work-id=85983352]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983352,"title":"Spekkens’s toy theory as a category of processes","internal_url":"https://www.academia.edu/85983352/Spekkens_s_toy_theory_as_a_category_of_processes","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535206,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535206/thumbnails/1.jpg","file_name":"1108.pdf","download_url":"https://www.academia.edu/attachments/90535206/download_file","bulk_download_file_name":"Spekkens_s_toy_theory_as_a_category_of_p.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535206/1108-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DSpekkens_s_toy_theory_as_a_category_of_p.pdf\u0026Expires=1740553109\u0026Signature=K9Qh7weVOPwfkiKjHQJ0Ct5wEtPPahrZ~Ai3FCZ98GWFkNpZ7BBQoZp1cvqfMiVrDPE-yBPVRKQsviz0AsRfeJHzY2TT7zKkQPwVeLSL0Z0lXPlnIyGVFJrUoYZfJBl3nGB7FeqKHuUQAvw5dLdGbPepe5dcg48cKcnFOvmAv6C3~2Tc3SW1ZKJ1EbtnIlv1Sq7NJZJDsLDsgAj9q5gppKQJI8alZr5GPWpujrE-dYvgGdkWeWaPdr5N-uqjLbSZ3nPVPSbSD43pH0HVQDGsUBuu2lG0g4QipZvg7k1BbOSVrO1U9YnIjtB5Bv5r7OY-hd0rJlmrNaeIVN4~xABqgw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983346"><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/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus"><img alt="Research paper thumbnail of Three qubit entanglement within graphical Z/X-calculus" class="work-thumbnail" src="https://attachments.academia-assets.com/90535190/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/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus">Three qubit entanglement within graphical Z/X-calculus</a></div><div class="wp-workCard_item"><span>Electronic Proceedings in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quan...</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">The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the Wand GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d742b6c25ba968d041f10149e750d3ab" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535190,"asset_id":85983346,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535190/download_file?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="85983346"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983346"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983346; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983346]").text(description); $(".js-view-count[data-work-id=85983346]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983346; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983346']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "d742b6c25ba968d041f10149e750d3ab" } } $('.js-work-strip[data-work-id=85983346]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983346,"title":"Three qubit entanglement within graphical Z/X-calculus","internal_url":"https://www.academia.edu/85983346/Three_qubit_entanglement_within_graphical_Z_X_calculus","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535190,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535190/thumbnails/1.jpg","file_name":"1103.pdf","download_url":"https://www.academia.edu/attachments/90535190/download_file","bulk_download_file_name":"Three_qubit_entanglement_within_graphica.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535190/1103-libre.pdf?1662037465=\u0026response-content-disposition=attachment%3B+filename%3DThree_qubit_entanglement_within_graphica.pdf\u0026Expires=1740553109\u0026Signature=Kq1Zz1cPW-McHTbhYPoKVpSXwXO~5uH4NWZyyzhN6PLUCA5t4iXCe118X3QA5pPfMQxF7HqTpiBiVJIeNMHNk1L3jN9INh37KLacDbB4MppN7mj2AHsncb6TOXwpuZ5c8kEAoLeGTh6RSX-jTHmXK9SjUOCIhIyD4gb609ZX78itk4ramocUCQVDQ3YP8tDDuvadnYoRTbkRSC97o1CsmjvaAIfR-iuqHFIKfug5siT~GlVD2~JZykuNkXkExIcgz~Ajw5TsR5heCo0md~4PAYBIYmnygjf-0HVfBOBY89j~9HmWoYVKDNkMSECiNRk5VclXRciPbnwzxQ6OEVBPaw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983341"><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/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time"><img alt="Research paper thumbnail of Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time" class="work-thumbnail" src="https://attachments.academia-assets.com/90535189/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/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time">Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time</a></div><div class="wp-workCard_item"><span>Physical Review Letters</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">There is an incompatibility between the symmetries of causal structure in relativity theory and 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">There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time-reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with space-like separated input-output pairs. We explicitly describe a nonsignaling device which becomes a perfect signaling device under time-reversal, where time-reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although time-reversal of Popuscu-Rörlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time-reversal using post-selection, which could lead experimental implementation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f6eac72f55834193b76e1288e4f1ceff" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535189,"asset_id":85983341,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535189/download_file?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="85983341"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983341"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983341; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983341]").text(description); $(".js-view-count[data-work-id=85983341]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983341; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983341']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "f6eac72f55834193b76e1288e4f1ceff" } } $('.js-work-strip[data-work-id=85983341]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983341,"title":"Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time","internal_url":"https://www.academia.edu/85983341/Time_Asymmetry_of_Probabilities_Versus_Relativistic_Causal_Structure_An_Arrow_of_Time","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535189,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535189/thumbnails/1.jpg","file_name":"1108.pdf","download_url":"https://www.academia.edu/attachments/90535189/download_file","bulk_download_file_name":"Time_Asymmetry_of_Probabilities_Versus_R.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535189/1108-libre.pdf?1662037463=\u0026response-content-disposition=attachment%3B+filename%3DTime_Asymmetry_of_Probabilities_Versus_R.pdf\u0026Expires=1740553109\u0026Signature=ap9NxFN5MdIg1kPjkgit46RI37CEka5h2zTBsHKU7QzmN0Ii3g7K1Ch4hQWjUjEWWSbtUeB8~tBL6g1XomjHiOqpR3afKkrimr6eVXPbuaMPryQXfQsgKOsd7w2KZF5WzWb1FuNEKDbeEpOxja5yITn9ctdODGGVKSb3WBq2rzmtkeDybwTSKcOaGh8Tfw-i6QTOpdsUiQykTUVd1yYwqZ9ner6Hbq7RaDLJTJGRrikim8wGZw5ORH~G5qd2q~ulziKukaSpIO9rn6KlZoOGcA~Fnx0WlVVD6-khyr99m~bDeFeEAriGDLIa6iqvR60MJkY0RxBSzcxbgYbTl3hFyw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983337"><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/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics"><img alt="Research paper thumbnail of Interacting quantum observables: categorical algebra and diagrammatics" class="work-thumbnail" src="https://attachments.academia-assets.com/90535188/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/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics">Interacting quantum observables: categorical algebra and diagrammatics</a></div><div class="wp-workCard_item"><span>New Journal of Physics</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphica...</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 paper has two tightly intertwined aims: (i) To introduce an intuitive and universal graphical calculus for multi-qubit systems, the zx-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatise complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z and X spin observables, which yields a scaled variant of a bialgebra.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4a6bdfb47f73d5aea5364bb4295be582" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535188,"asset_id":85983337,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535188/download_file?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="85983337"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983337"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983337; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983337]").text(description); $(".js-view-count[data-work-id=85983337]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983337; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983337']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "4a6bdfb47f73d5aea5364bb4295be582" } } $('.js-work-strip[data-work-id=85983337]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983337,"title":"Interacting quantum observables: categorical algebra and diagrammatics","internal_url":"https://www.academia.edu/85983337/Interacting_quantum_observables_categorical_algebra_and_diagrammatics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535188,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535188/thumbnails/1.jpg","file_name":"0906.pdf","download_url":"https://www.academia.edu/attachments/90535188/download_file","bulk_download_file_name":"Interacting_quantum_observables_categori.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535188/0906-libre.pdf?1662037508=\u0026response-content-disposition=attachment%3B+filename%3DInteracting_quantum_observables_categori.pdf\u0026Expires=1740553109\u0026Signature=GRu5k5kFRy2E8-gXJwXMpnej9Z8ev8htAnQU3SLKDa3RRYul9cSpHQIsfH8B5tZEZND4IaKujZ3Uiet34FGaiOhLXwBpChUGhC6SrEY5ywOpswDZPhGYI3aZBCwS2hXRO90InZNqY9sp8ko3J7cuMAWX3vcSHfmazXuMkrLxOSTlc6buGLd-1VIfDsg9fWbJMoh5WRawzosBbx1vmtt0X-pV8stNUIOUpZEqrikK5BWwYeHOVg9SO5SIXLTVFdxSyaJ0DA3cXZ6YeHGsBuewuNnAnHKprjC1eCelTCvh-Tx5g9PMl1jz8lWXy4vLwQncMStnI68aE3R10RDwfarEwA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983327"><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/85983327/Causal_Categories_Relativistically_Interacting_Processes"><img alt="Research paper thumbnail of Causal Categories: Relativistically Interacting Processes" class="work-thumbnail" src="https://attachments.academia-assets.com/90535181/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/85983327/Causal_Categories_Relativistically_Interacting_Processes">Causal Categories: Relativistically Interacting Processes</a></div><div class="wp-workCard_item"><span>Foundations of Physics</span><span>, 2012</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A symmetric monoidal category naturally arises as the mathematical structure that organizes physi...</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">A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4c3f84eb76f5f69472ad3900626cf28e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535181,"asset_id":85983327,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535181/download_file?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="85983327"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983327"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983327; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983327]").text(description); $(".js-view-count[data-work-id=85983327]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983327; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983327']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "4c3f84eb76f5f69472ad3900626cf28e" } } $('.js-work-strip[data-work-id=85983327]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983327,"title":"Causal Categories: Relativistically Interacting Processes","internal_url":"https://www.academia.edu/85983327/Causal_Categories_Relativistically_Interacting_Processes","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535181,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535181/thumbnails/1.jpg","file_name":"1107.pdf","download_url":"https://www.academia.edu/attachments/90535181/download_file","bulk_download_file_name":"Causal_Categories_Relativistically_Inter.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535181/1107-libre.pdf?1662037476=\u0026response-content-disposition=attachment%3B+filename%3DCausal_Categories_Relativistically_Inter.pdf\u0026Expires=1740553109\u0026Signature=Ee6RaCiX5IbqO3iYpb3HnKCsIxByx~gSE1P2oSps9cbblZuuzftODeK5Chm4w7HMXtyn3pXVi0woDAVAjEmUDXPzyavuwDo8oKG47ZgKQWApeXu4SsgGyIydazitDznzvGBNu~JEedw3gosiT~SNsbuyHWgk6rUItOisnbg5UOS3r86~j6gQmZ6zMGcsjxCHPGK8vWLUPmdCdwRpnG4q96xtsvx0fmXX~mOqH1o5DR~-c2ff3j1lC5OrGSNlbVOylSev5ogQyqQGNhY6cOQIaTUgt9yD4XWvFY5gR1nw59LAWyVl7YMlAVby7dxvJluXGLy7OYQ-B-eL1oXb72qu1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983320"><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/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_"><img alt="Research paper thumbnail of Graphical Calculus for Quantum Key Distribution (Extended Abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/90535171/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/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_">Graphical Calculus for Quantum Key Distribution (Extended Abstract)</a></div><div class="wp-workCard_item"><span>Electronic Notes in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Controlled complementary measurements are key to quantum key distribution protocols, among many 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">Controlled complementary measurements are key to quantum key distribution protocols, among many other things. We axiomatize controlled complementary measurements within symmetric monoidal categories, which provides them with a corresponding graphical calculus. We study the BB84 and Ekert91 protocols within this calculus, including the case where there is an intercept-resend attack.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="a5909da1d21aca4d6ccfcac07e32b32f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535171,"asset_id":85983320,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535171/download_file?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="85983320"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983320"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983320; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983320]").text(description); $(".js-view-count[data-work-id=85983320]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983320; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983320']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "a5909da1d21aca4d6ccfcac07e32b32f" } } $('.js-work-strip[data-work-id=85983320]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983320,"title":"Graphical Calculus for Quantum Key Distribution (Extended Abstract)","internal_url":"https://www.academia.edu/85983320/Graphical_Calculus_for_Quantum_Key_Distribution_Extended_Abstract_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535171,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535171/thumbnails/1.jpg","file_name":"82074856.pdf","download_url":"https://www.academia.edu/attachments/90535171/download_file","bulk_download_file_name":"Graphical_Calculus_for_Quantum_Key_Distr.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535171/82074856-libre.pdf?1662037472=\u0026response-content-disposition=attachment%3B+filename%3DGraphical_Calculus_for_Quantum_Key_Distr.pdf\u0026Expires=1740553109\u0026Signature=UK8-APUr9d4EUm7v145j-mesSC4x0QWfcdpheCwbcHOD8f2VXra1qsGpxZ89ZDM~iYR~FG-Y032HeMjjgSZ1g13np8CLg9OkgdkFmFe4Tmu1V1qBxgpqkfmrGd5rgCsp0Tw~H4ycdBHu4VE5PLI~dYLRHHBlPvr5vhiwOpJJkYGtxSDYY2-u6PNIFQlTDZCnFmWBBLT~Eon8zjXSc1yx7-y49x4i2c6PaPEPEN6FeUh3C4jGNlDp9N83wAGBems0TuEQHeEt4bPU64jLuzxR9cqSJrLaErZNic-iSM39tK2OA3sGEqpILPwZWViYBYATPz7owFPYrzzX4rMRXwOy5w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983313"><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/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning"><img alt="Research paper thumbnail of Towards a Compositional Distributional Model of Meaning" class="work-thumbnail" src="https://attachments.academia-assets.com/90535160/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/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning">Towards a Compositional Distributional Model of Meaning</a></div><div class="wp-workCard_item"><span>comlab.ox.ac.uk</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We propose a mathematical framework for a unifica-tion of the distributional theory of meaning in...</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 propose a mathematical framework for a unifica-tion of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, namely Lambek&#x27;s pregroup seman-tics. A key observation is that the monoidal category of (finite ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="edc347ee114b0280ef13fe1fda806c9f" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535160,"asset_id":85983313,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535160/download_file?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="85983313"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983313"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983313; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983313]").text(description); $(".js-view-count[data-work-id=85983313]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983313; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983313']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "edc347ee114b0280ef13fe1fda806c9f" } } $('.js-work-strip[data-work-id=85983313]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983313,"title":"Towards a Compositional Distributional Model of Meaning","internal_url":"https://www.academia.edu/85983313/Towards_a_Compositional_Distributional_Model_of_Meaning","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535160,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535160/thumbnails/1.jpg","file_name":"AAAI_2008.pdf","download_url":"https://www.academia.edu/attachments/90535160/download_file","bulk_download_file_name":"Towards_a_Compositional_Distributional_M.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535160/AAAI_2008-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DTowards_a_Compositional_Distributional_M.pdf\u0026Expires=1740553109\u0026Signature=RiovyLzD0N3uE2ym3oGlKlqG49V2mp~yd55MoQ0arRAIllIhFH-TfbJTMqx0E0bzD5P1Ilw3mqocVbqE2XbwyATVsPjpqIwDfKoK94BfeX~JcuX69ZEATj3QLsx2f5VUS-fvi62sk~3YvzSrMFlTnyKWyiRcy7bCrpAt0PcfH8jbI52fU~07yXlwoC8uQE1VjxEQ10SsxvYPjSDSHdhCznumhxAPn3SZCR-pW83qshpvl5X6L0jiXgiLiTV1dyCr5x8FQ2ufsCVIrQAJMTM7mIkDeK~K2VZggYNw1cpDpMSwEyDo1N~ooNSvQIRtydqeSZoI1oBNZKMhZMcFAGYhog__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983306"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_"><img alt="Research paper thumbnail of Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.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" rel="nofollow" href="https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_">Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)</a></div><div class="wp-workCard_item"><span>atlas-conferences.com</span><span>, 2007</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLAS...</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">Atlas home || Conferences | Abstracts | about Atlas ALGEBRAIC AND TOPOLOGICAL METHODS IN NON-CLASSICAL LOGICS III (TANCL&#x27;07) August 5-9, 2007 St Anne&#x27;s College, University of Oxford Oxford, England. Organizers Mai Gehrke and Hilary Priestley. Conference Homepage. Abstracts. SAMSON ABRAMSKY Domain Theory in Logical Form Revisited: a 20-year Retrospective Stefano Aguzzoli Goedel algebras free over finite distributive ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><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="85983306"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983306"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983306; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983306]").text(description); $(".js-view-count[data-work-id=85983306]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983306; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983306']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=85983306]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983306,"title":"Algebraic and Topological Methods in Non-Classical Logics III (TANCL'07)","internal_url":"https://www.academia.edu/85983306/Algebraic_and_Topological_Methods_in_Non_Classical_Logics_III_TANCL07_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[]}, 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="85983300"><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/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences"><img alt="Research paper thumbnail of Diagrammatic Reasoning about Meaning of Sentences" class="work-thumbnail" src="https://attachments.academia-assets.com/90535147/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/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences">Diagrammatic Reasoning about Meaning of Sentences</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The symbolic [5] and distributional [8] theories of meaning are somewhat orthogonal with competin...</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">The symbolic [5] and distributional [8] theories of meaning are somewhat orthogonal with competing pros and cons: the former is compositional but only qualitative, the latter is non-compositional but quantitative. Following [9] in the context of Cognitive Science, where a similar problem exists between the connectionist and symbolic models of mind,[3] argued for the use of the tensor product of vector spaces and pairing the vectors of meaning with their syntactic roles. This abstract summarizes the framework developed in [2], which builds on ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="aa2d1af71b2d470fd0598d3b31d8001e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535147,"asset_id":85983300,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535147/download_file?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="85983300"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983300"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983300; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983300]").text(description); $(".js-view-count[data-work-id=85983300]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983300; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983300']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "aa2d1af71b2d470fd0598d3b31d8001e" } } $('.js-work-strip[data-work-id=85983300]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983300,"title":"Diagrammatic Reasoning about Meaning of Sentences","internal_url":"https://www.academia.edu/85983300/Diagrammatic_Reasoning_about_Meaning_of_Sentences","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535147,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535147/thumbnails/1.jpg","file_name":"distcomp2010_clark_etal_9.pdf","download_url":"https://www.academia.edu/attachments/90535147/download_file","bulk_download_file_name":"Diagrammatic_Reasoning_about_Meaning_of.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535147/distcomp2010_clark_etal_9-libre.pdf?1662037471=\u0026response-content-disposition=attachment%3B+filename%3DDiagrammatic_Reasoning_about_Meaning_of.pdf\u0026Expires=1740553109\u0026Signature=SzSMzFPu8PQ~lFLDAuwZiYqzKqPdsVvvSHvG05~NO7gsDzYeRZUsgTecT-HizEJ9VR6vk-uimpxdAo1X4tS3HiU2ZElV34Fjsx82eiddMRt5JGH3eX9zpE2tJKgjxf2X1i9-wj-fLovOn1UttZkouFaY69mjL6WjmxqJG0eleYrs-c9Yay0E~8wGNcS3i7bA1xFXEOCrmE~LR1rZcel0kfGzED-KxgxK0iIB83qQaNgtIXH~GIKXblVWdPHw9FOfa8095oqZqV4CXMTkxYMw5HRYxEBjjS-ERpN3dHrepBlzVFYIvn5olU-htlesh9nQ50hNaKq2zWy3xwOiSqXtnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983296"><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/85983296/Partiality_in_physics"><img alt="Research paper thumbnail of Partiality in physics" class="work-thumbnail" src="https://attachments.academia-assets.com/90535140/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/85983296/Partiality_in_physics">Partiality in physics</a></div><div class="wp-workCard_item"><span>arXiv preprint quant-ph/0312044</span><span>, Dec 4, 2003</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Abstract: We revisit the standard axioms of domain theory with emphasis on their relation to the ...</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">Abstract: We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting capable of providing a satisfactory unification of the two.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="0c993d8f1734040b9fd6f263c3683063" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535140,"asset_id":85983296,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535140/download_file?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="85983296"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983296"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983296; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983296]").text(description); $(".js-view-count[data-work-id=85983296]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983296; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983296']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "0c993d8f1734040b9fd6f263c3683063" } } $('.js-work-strip[data-work-id=85983296]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983296,"title":"Partiality in physics","internal_url":"https://www.academia.edu/85983296/Partiality_in_physics","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535140,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535140/thumbnails/1.jpg","file_name":"0312044.pdf","download_url":"https://www.academia.edu/attachments/90535140/download_file","bulk_download_file_name":"Partiality_in_physics.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535140/0312044-libre.pdf?1662037478=\u0026response-content-disposition=attachment%3B+filename%3DPartiality_in_physics.pdf\u0026Expires=1740553109\u0026Signature=aQ5W2u5x81QfLkySnWWJHTFkBKfBTNe8WXjfNVtg7lin0-Rb7tr324PJ8AGJRBJJGzc2z~Yw8MzyTB-Gel20dSaVUImfcKF4v3tg48dagKiziarFnJ6EkHRxLZ9gSNi53ogwRirvinZRQ1PmQHNjAWHRxqGfOwUg4PtYo2~LFjUHCJkEluk4AdhqzsCkRRbaPa2a8Nbn~08OhVmhxofwsoHwlP8l~3D86ss8gBbA4eHOAPrq54uRhavUo3ejjSsHw1ilXMhKoV7V3iTY~ym-TQpkdk4d6bFqiHJdRn9ULoixXRNRfJ3U8LZfAoRz0~ovNEvOhZaHyTKZhnlGWXkPXw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="85983232"><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/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras"><img alt="Research paper thumbnail of Reasoning about meaning in natural language with compact closed categories and Frobenius algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/90535104/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/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras">Reasoning about meaning in natural language with compact closed categories and Frobenius algebras</a></div><div class="wp-workCard_item"><span>Logic and Algebraic Structures in Quantum Computing</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Compact closed categories have found applications in modeling quantum information protocols by Ab...</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">Compact closed categories have found applications in modeling quantum information protocols by Abramsky-Coecke. They also provide semantics for Lambek's pregroup algebras, applied to formalizing the grammatical structure of natural language, and are implicit in a distributional model of word meaning based on vector spaces. Specifically, in previous work Coecke-Clark-Sadrzadeh used the product category of pregroups with vector spaces and provided a distributional model of meaning for sentences. We recast this theory in terms of strongly monoidal functors and advance it via Frobenius algebras over vector spaces. The former are used to formalize topological quantum field theories by Atiyah and Baez-Dolan, and the latter are used to model classical data in quantum protocols by Coecke-Pavlovic-Vicary. The Frobenius algebras enable us to work in a single space in which meanings of words, phrases, and sentences of any structure live. Hence we can compare meanings of different language constructs and enhance the applicability of the theory. We report on experimental results on a number of language tasks and verify the theoretical predictions.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="fb20aeb0d7210d01a63058ff4e19458a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":90535104,"asset_id":85983232,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/90535104/download_file?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="85983232"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="85983232"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 85983232; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=85983232]").text(description); $(".js-view-count[data-work-id=85983232]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 85983232; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='85983232']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "fb20aeb0d7210d01a63058ff4e19458a" } } $('.js-work-strip[data-work-id=85983232]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":85983232,"title":"Reasoning about meaning in natural language with compact closed categories and Frobenius algebras","internal_url":"https://www.academia.edu/85983232/Reasoning_about_meaning_in_natural_language_with_compact_closed_categories_and_Frobenius_algebras","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":90535104,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/90535104/thumbnails/1.jpg","file_name":"1401.5980.pdf","download_url":"https://www.academia.edu/attachments/90535104/download_file","bulk_download_file_name":"Reasoning_about_meaning_in_natural_langu.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/90535104/1401.5980-libre.pdf?1662037482=\u0026response-content-disposition=attachment%3B+filename%3DReasoning_about_meaning_in_natural_langu.pdf\u0026Expires=1740553109\u0026Signature=JBiGX5rnNwSiOqLcCbvt5exBsub9-MgkiaobafnIjnUQtaj7fIFcMJCTgv-3MMqhOSMHmVdfk9qELoDA4OP~jEVL3sO1lbO-unJXHgAliCfl1Rkw03PMv-ux~K9-GmY1ydCpk~i0GFogI7bqAP7U24yx62mhIdOywN7Qcy7GaOmVS7sqPRgx7y0wvek9rMJtchP-cKC4f7ZamStg0nmy9tsiaNS-oma~-uM1kAVIx4XG6f4JdrLkSkm0SHMXbFwr2VqWiXPQ9ljAtLIv1LKmgc9a~Ikd9nMqGlC8rzhz7Mls-y4HR4-ECHLD~h0dw310t2ZL0rpM06Oav0wdWJ5erw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, 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="80860334"><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/80860334/Toy_Quantum_Categories_Extended_Abstract_"><img alt="Research paper thumbnail of Toy Quantum Categories (Extended Abstract)" class="work-thumbnail" src="https://attachments.academia-assets.com/87101250/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/80860334/Toy_Quantum_Categories_Extended_Abstract_">Toy Quantum Categories (Extended Abstract)</a></div><div class="wp-workCard_item"><span>Electronic Notes in Theoretical Computer Science</span><span>, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach 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 that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set in FRel.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="add920fcde17596377a6c31c1168715a" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":87101250,"asset_id":80860334,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/87101250/download_file?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="80860334"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="80860334"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 80860334; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=80860334]").text(description); $(".js-view-count[data-work-id=80860334]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 80860334; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='80860334']"); 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></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.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: "add920fcde17596377a6c31c1168715a" } } $('.js-work-strip[data-work-id=80860334]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":80860334,"title":"Toy Quantum Categories (Extended Abstract)","internal_url":"https://www.academia.edu/80860334/Toy_Quantum_Categories_Extended_Abstract_","owner_id":112917,"coauthors_can_edit":true,"owner":{"id":112917,"first_name":"Bob","middle_initials":null,"last_name":"Coecke","page_name":"BobCoecke","domain_name":"oxford","created_at":"2010-01-08T18:32:13.484-08:00","display_name":"Bob Coecke","url":"https://oxford.academia.edu/BobCoecke"},"attachments":[{"id":87101250,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/87101250/thumbnails/1.jpg","file_name":"82443403.pdf","download_url":"https://www.academia.edu/attachments/87101250/download_file","bulk_download_file_name":"Toy_Quantum_Categories_Extended_Abstract.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/87101250/82443403-libre.pdf?1654548069=\u0026response-content-disposition=attachment%3B+filename%3DToy_Quantum_Categories_Extended_Abstract.pdf\u0026Expires=1740553109\u0026Signature=VkipwGOFuIEjj13zD0jb76VBWAVvvN3By6iGQewMFu61eWhtKx-mBlG6owYE6KKShOEzJDdTGRanM0mZXOEvLKvryap9JY6Hsf4yGvX0IsHPvZ6ZCza4e3dQPoYr~PKhomKbDVG5YS77CMWuaPJ44hpXipLrdpKbJBIb4hBRQHa~Q8~aIDhquO9ekT9SpjFOMQGdLVzk4z9wESfNwgu35zL20MKD~4CJXBWKeOsfWmDp4Jml~NqMW6M1pHk7pl2GZ8ddn3F7Nj-4Wu5WgrQtJ-v~SI7qray8bmGi92KJ6U08QjeHS1aIZjnfUI6G7lLPCGIXbuBMu7sDzbXYSzcXnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/google_contacts-0dfb882d836b94dbcb4a2d123d6933fc9533eda5be911641f20b4eb428429600.js"], function() { // from javascript_helper.rb $('.js-google-connect-button').click(function(e) { e.preventDefault(); GoogleContacts.authorize_and_show_contacts(); Aedu.Dismissibles.recordClickthrough("WowProfileImportContactsPrompt"); }); $('.js-update-biography-button').click(function(e) { e.preventDefault(); Aedu.Dismissibles.recordClickthrough("UpdateUserBiographyPrompt"); $.ajax({ url: $r.api_v0_profiles_update_about_path({ subdomain_param: 'api', about: "", }), type: 'PUT', success: function(response) { location.reload(); } }); }); $('.js-work-creator-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_document_path({ source: encodeURIComponent(""), }); }); $('.js-video-upload-button').click(function (e) { e.preventDefault(); window.location = $r.upload_funnel_video_path({ source: encodeURIComponent(""), }); }); $('.js-do-this-later-button').click(function() { $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("WowProfileImportContactsPrompt"); }); $('.js-update-biography-do-this-later-button').click(function(){ $(this).closest('.js-profile-nag-panel').remove(); Aedu.Dismissibles.recordDismissal("UpdateUserBiographyPrompt"); }); $('.wow-profile-mentions-upsell--close').click(function(){ $('.wow-profile-mentions-upsell--panel').hide(); Aedu.Dismissibles.recordDismissal("WowProfileMentionsUpsell"); }); $('.wow-profile-mentions-upsell--button').click(function(){ Aedu.Dismissibles.recordClickthrough("WowProfileMentionsUpsell"); }); new WowProfile.SocialRedesignUserWorks({ initialWorksOffset: 20, allWorksOffset: 20, maxSections: 1 }) }); </script> </div></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile_edit-5ea339ee107c863779f560dd7275595239fed73f1a13d279d2b599a28c0ecd33.js","https://a.academia-assets.com/assets/add_coauthor-22174b608f9cb871d03443cafa7feac496fb50d7df2d66a53f5ee3c04ba67f53.js","https://a.academia-assets.com/assets/tab-dcac0130902f0cc2d8cb403714dd47454f11fc6fb0e99ae6a0827b06613abc20.js","https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js"], function() { // from javascript_helper.rb window.ae = window.ae || {}; window.ae.WowProfile = window.ae.WowProfile || {}; if(Aedu.User.current && Aedu.User.current.id === $viewedUser.id) { window.ae.WowProfile.current_user_edit = {}; new WowProfileEdit.EditUploadView({ el: '.js-edit-upload-button-wrapper', model: window.$current_user, }); new AddCoauthor.AddCoauthorsController(); } var userInfoView = new WowProfile.SocialRedesignUserInfo({ recaptcha_key: "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB" }); WowProfile.router = new WowProfile.Router({ userInfoView: userInfoView }); Backbone.history.start({ pushState: true, root: "/" + $viewedUser.page_name }); new WowProfile.UserWorksNav() }); </script> </div> <div class="bootstrap login"><div class="modal fade login-modal" id="login-modal"><div class="login-modal-dialog modal-dialog"><div class="modal-content"><div class="modal-header"><button class="close close" data-dismiss="modal" type="button"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button><h4 class="modal-title text-center"><strong>Log In</strong></h4></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><button class="btn btn-fb btn-lg btn-block btn-v-center-content" id="login-facebook-oauth-button"><svg style="float: left; width: 19px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="facebook-square" class="svg-inline--fa fa-facebook-square fa-w-14" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path fill="currentColor" d="M400 32H48A48 48 0 0 0 0 80v352a48 48 0 0 0 48 48h137.25V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.27c-30.81 0-40.42 19.12-40.42 38.73V256h68.78l-11 71.69h-57.78V480H400a48 48 0 0 0 48-48V80a48 48 0 0 0-48-48z"></path></svg><small><strong>Log in</strong> with <strong>Facebook</strong></small></button><br /><button class="btn btn-google btn-lg btn-block btn-v-center-content" id="login-google-oauth-button"><svg style="float: left; width: 22px; line-height: 1em; margin-right: .3em;" aria-hidden="true" focusable="false" data-prefix="fab" data-icon="google-plus" class="svg-inline--fa fa-google-plus fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256,8C119.1,8,8,119.1,8,256S119.1,504,256,504,504,392.9,504,256,392.9,8,256,8ZM185.3,380a124,124,0,0,1,0-248c31.3,0,60.1,11,83,32.3l-33.6,32.6c-13.2-12.9-31.3-19.1-49.4-19.1-42.9,0-77.2,35.5-77.2,78.1S142.3,334,185.3,334c32.6,0,64.9-19.1,70.1-53.3H185.3V238.1H302.2a109.2,109.2,0,0,1,1.9,20.7c0,70.8-47.5,121.2-118.8,121.2ZM415.5,273.8v35.5H380V273.8H344.5V238.3H380V202.8h35.5v35.5h35.2v35.5Z"></path></svg><small><strong>Log in</strong> with <strong>Google</strong></small></button><br /><style type="text/css">.sign-in-with-apple-button { width: 100%; height: 52px; border-radius: 3px; border: 1px solid black; cursor: pointer; } .sign-in-with-apple-button > div { margin: 0 auto; / This centers the Apple-rendered button horizontally }</style><script src="https://appleid.cdn-apple.com/appleauth/static/jsapi/appleid/1/en_US/appleid.auth.js" type="text/javascript"></script><div class="sign-in-with-apple-button" data-border="false" data-color="white" id="appleid-signin"><span   ="Sign Up with Apple" class="u-fs11"></span></div><script>AppleID.auth.init({ clientId: 'edu.academia.applesignon', scope: 'name email', redirectURI: 'https://www.academia.edu/sessions', state: "5f231b112040948cffc86361664a2d20dcc16cd7c6758d25833162635d2eb83a", });</script><script>// Hacky way of checking if on fast loswp if (window.loswp == null) { (function() { const Google = window?.Aedu?.Auth?.OauthButton?.Login?.Google; const Facebook = window?.Aedu?.Auth?.OauthButton?.Login?.Facebook; if (Google) { new Google({ el: '#login-google-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } if (Facebook) { new Facebook({ el: '#login-facebook-oauth-button', rememberMeCheckboxId: 'remember_me', track: null }); } })(); }</script></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><div class="hr-heading login-hr-heading"><span class="hr-heading-text">or</span></div></div></div></div><div class="modal-body"><div class="row"><div class="col-xs-10 col-xs-offset-1"><form class="js-login-form" action="https://www.academia.edu/sessions" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="_b2gl0glzoP3AYJrvIqJ2InNVvmNnyETWN9g_9ZqFvFz13DtXibydT8fUT-fm3zE8tDeL765kp4OOcDV9oM5tQ" autocomplete="off" /><div class="form-group"><label class="control-label" for="login-modal-email-input" style="font-size: 14px;">Email</label><input class="form-control" id="login-modal-email-input" name="login" type="email" /></div><div class="form-group"><label class="control-label" for="login-modal-password-input" style="font-size: 14px;">Password</label><input class="form-control" id="login-modal-password-input" name="password" type="password" /></div><input type="hidden" name="post_login_redirect_url" id="post_login_redirect_url" value="https://oxford.academia.edu/BobCoecke" autocomplete="off" /><div class="checkbox"><label><input type="checkbox" name="remember_me" id="remember_me" value="1" checked="checked" /><small style="font-size: 12px; margin-top: 2px; display: inline-block;">Remember me on this computer</small></label></div><br><input type="submit" name="commit" value="Log In" class="btn btn-primary btn-block btn-lg js-login-submit" data-disable-with="Log In" /></br></form><script>typeof window?.Aedu?.recaptchaManagedForm === 'function' && window.Aedu.recaptchaManagedForm( document.querySelector('.js-login-form'), document.querySelector('.js-login-submit') );</script><small style="font-size: 12px;"><br />or <a data-target="#login-modal-reset-password-container" data-toggle="collapse" href="javascript:void(0)">reset password</a></small><div class="collapse" id="login-modal-reset-password-container"><br /><div class="well margin-0x"><form class="js-password-reset-form" action="https://www.academia.edu/reset_password" accept-charset="UTF-8" method="post"><input type="hidden" name="authenticity_token" value="hnIt7aApYwAnB62pLsuKiz-79hG2_2AQxRayBFhcwdgIGP2Xtipf9u8Zfv0N2n-XRKZ-x4XZ052T8BIueLXunA" autocomplete="off" /><p>Enter the email address you signed up with and we'll email you a reset link.</p><div class="form-group"><input class="form-control" name="email" type="email" /></div><script src="https://recaptcha.net/recaptcha/api.js" async defer></script> <script> var invisibleRecaptchaSubmit = function () { var closestForm = function (ele) { var curEle = ele.parentNode; while (curEle.nodeName !== 'FORM' && curEle.nodeName !== 'BODY'){ curEle = curEle.parentNode; } return curEle.nodeName === 'FORM' ? curEle : null }; var eles = document.getElementsByClassName('g-recaptcha'); if (eles.length > 0) { var form = closestForm(eles[0]); if (form) { form.submit(); } } }; </script> <input type="submit" data-sitekey="6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj" data-callback="invisibleRecaptchaSubmit" class="g-recaptcha btn btn-primary btn-block" value="Email me a link" value=""/> </form></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/collapse-45805421cf446ca5adf7aaa1935b08a3a8d1d9a6cc5d91a62a2a3a00b20b3e6a.js"], function() { // from javascript_helper.rb $("#login-modal-reset-password-container").on("shown.bs.collapse", function() { $(this).find("input[type=email]").focus(); }); }); </script> </div></div></div><div class="modal-footer"><div class="text-center"><small style="font-size: 12px;">Need an account? <a rel="nofollow" href="https://www.academia.edu/signup">Click here to sign up</a></small></div></div></div></div></div></div><script>// If we are on subdomain or non-bootstrapped page, redirect to login page instead of showing modal (function(){ if (typeof $ === 'undefined') return; var host = window.location.hostname; if ((host === $domain || host === "www."+$domain) && (typeof $().modal === 'function')) { $("#nav_log_in").click(function(e) { // Don't follow the link and open the modal e.preventDefault(); $("#login-modal").on('shown.bs.modal', function() { $(this).find("#login-modal-email-input").focus() }).modal('show'); }); } })()</script> <div class="bootstrap" id="footer"><div class="footer-content clearfix text-center padding-top-7x" style="width:100%;"><ul class="footer-links-secondary footer-links-wide list-inline margin-bottom-1x"><li><a href="https://www.academia.edu/about">About</a></li><li><a href="https://www.academia.edu/press">Press</a></li><li><a href="https://www.academia.edu/documents">Papers</a></li><li><a href="https://www.academia.edu/topics">Topics</a></li><li><a href="https://www.academia.edu/journals">Academia.edu Journals</a></li><li><a rel="nofollow" href="https://www.academia.edu/hiring"><svg style="width: 13px; height: 13px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="briefcase" class="svg-inline--fa fa-briefcase fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M320 336c0 8.84-7.16 16-16 16h-96c-8.84 0-16-7.16-16-16v-48H0v144c0 25.6 22.4 48 48 48h416c25.6 0 48-22.4 48-48V288H320v48zm144-208h-80V80c0-25.6-22.4-48-48-48H176c-25.6 0-48 22.4-48 48v48H48c-25.6 0-48 22.4-48 48v80h512v-80c0-25.6-22.4-48-48-48zm-144 0H192V96h128v32z"></path></svg> <strong>We're Hiring!</strong></a></li><li><a rel="nofollow" href="https://support.academia.edu/hc/en-us"><svg style="width: 12px; height: 12px;" aria-hidden="true" focusable="false" data-prefix="fas" data-icon="question-circle" class="svg-inline--fa fa-question-circle fa-w-16" role="img" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M504 256c0 136.997-111.043 248-248 248S8 392.997 8 256C8 119.083 119.043 8 256 8s248 111.083 248 248zM262.655 90c-54.497 0-89.255 22.957-116.549 63.758-3.536 5.286-2.353 12.415 2.715 16.258l34.699 26.31c5.205 3.947 12.621 3.008 16.665-2.122 17.864-22.658 30.113-35.797 57.303-35.797 20.429 0 45.698 13.148 45.698 32.958 0 14.976-12.363 22.667-32.534 33.976C247.128 238.528 216 254.941 216 296v4c0 6.627 5.373 12 12 12h56c6.627 0 12-5.373 12-12v-1.333c0-28.462 83.186-29.647 83.186-106.667 0-58.002-60.165-102-116.531-102zM256 338c-25.365 0-46 20.635-46 46 0 25.364 20.635 46 46 46s46-20.636 46-46c0-25.365-20.635-46-46-46z"></path></svg> <strong>Help Center</strong></a></li></ul><ul class="footer-links-tertiary list-inline margin-bottom-1x"><li class="small">Find new research papers in:</li><li class="small"><a href="https://www.academia.edu/Documents/in/Physics">Physics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Chemistry">Chemistry</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Biology">Biology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Health_Sciences">Health Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Ecology">Ecology</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Earth_Sciences">Earth Sciences</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Cognitive_Science">Cognitive Science</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a></li><li class="small"><a href="https://www.academia.edu/Documents/in/Computer_Science">Computer Science</a></li></ul></div></div><div class="DesignSystem" id="credit" style="width:100%;"><ul class="u-pl0x footer-links-legal list-inline"><li><a rel="nofollow" href="https://www.academia.edu/terms">Terms</a></li><li><a rel="nofollow" href="https://www.academia.edu/privacy">Privacy</a></li><li><a rel="nofollow" href="https://www.academia.edu/copyright">Copyright</a></li><li>Academia ©2025</li></ul></div><script> //<![CDATA[ window.detect_gmtoffset = true; window.Academia && window.Academia.set_gmtoffset && Academia.set_gmtoffset('/gmtoffset'); //]]> </script> <div id='overlay_background'></div> <div id='bootstrap-modal-container' class='bootstrap'></div> <div id='ds-modal-container' class='bootstrap DesignSystem'></div> <div id='full-screen-modal'></div> </div> </body> </html>