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{"documenter":{"julia_version":"1.11.2","generation_timestamp":"2025-01-16T07:11:01","documenter_version":"1.8.0"}}
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<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · Ket.jl</title><meta name="title" content="Home · Ket.jl"/><meta property="og:title" content="Home · Ket.jl"/><meta property="twitter:title" content="Home · Ket.jl"/><meta name="description" content="Documentation for Ket.jl."/><meta property="og:description" content="Documentation for Ket.jl."/><meta property="twitter:description" content="Documentation for Ket.jl."/><meta property="og:url" content="https://dev-ket.github.io/Ket.jl/"/><meta property="twitter:url" content="https://dev-ket.github.io/Ket.jl/"/><link rel="canonical" href="https://dev-ket.github.io/Ket.jl/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" 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href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href><img class="docs-light-only" src="assets/logo.svg" alt="Ket.jl logo"/><img class="docs-dark-only" src="assets/logo-dark.svg" alt="Ket.jl logo"/></a><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Related-libraries"><span>Related libraries</span></a></li></ul></li><li><a class="tocitem" href="api/">List of functions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/dev-ket/Ket.jl/blob/master/README.md" title="View source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p><a href="https://dev-ket.github.io/Ket.jl/dev/"><img src="https://dev-ket.github.io/Ket.jl/dev/assets/ket-jl-logo-dark-wide.svg" alt="Banner"/></a></p><p><a href="https://dev-ket.github.io/Ket.jl/dev/"><img src="https://img.shields.io/badge/docs-dev-blue.svg" alt="Dev"/></a></p><p>Ket is a toolbox for quantum information, nonlocality, and entanglement written in the Julia programming language. All its functions are designed to work with generic types, allowing one to use <code>Int64</code> or <code>Float64</code> for efficiency, or arbitrary precision types when needed. Wherever possible they can be also used for optimization with <a href="https://jump.dev/JuMP.jl/stable/">JuMP</a>. And everything is optimized to the last microsecond.</p><p>Highlights:</p><ul><li>Work with multipartite Bell inequalities, computing their local bounds and Tsirelson bounds with <code>local_bound</code> and <code>tsirelson_bound</code>, and transforming between Collins-Gisin, probability, and correlator representations with <code>tensor_collinsgisin</code>, <code>tensor_probability</code>, and <code>tensor_correlation</code>.</li><li>Work with bipartite entanglement by computing the relative entropy of entanglement, random robustness, or Schmidt number via <code>entanglement_entropy</code>, <code>random_robustness</code>, and <code>schmidt_number</code>. Under the hood these functions use the DPS hierarchy, which is also available in isolation via <code>_dps_constraints!</code>.</li><li>Generate MUBs and SIC-POVMs through <code>mub</code> and <code>sic_povm</code>.</li><li>Generate uniformly-distributed random states, unitaries, and POVMs with <code>random_state</code>, <code>random_unitary</code>, and <code>random_povm</code>.</li><li>Generate well-known families of quantum states, such as the Bell states, the GHZ state, the W state, and the super-singlet via <code>state_bell</code>, <code>state_ghz</code>, <code>state_w</code>, and <code>state_supersinglet</code>.</li><li>Work with multilinear algebra via utility functions such as <code>partial_trace</code>, <code>partial_transpose</code>, and <code>permute_systems</code>.</li><li>Generate kets with <code>ket</code>.</li></ul><p>For the full list of functions see the <a href="https://dev-ket.github.io/Ket.jl/dev/api/">documentation</a>.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>Ket is a registered Julia package, so it can be installed by typing</p><pre><code class="nohighlight hljs">]add Ket</code></pre><p>into the Julia REPL.</p><h2 id="Related-libraries"><a class="docs-heading-anchor" href="#Related-libraries">Related libraries</a><a id="Related-libraries-1"></a><a class="docs-heading-anchor-permalink" href="#Related-libraries" title="Permalink"></a></h2><p>Julia: &lt;!–- <a href="https://github.com/ZIB-IOL/BellPolytopes.jl">BellPolytopes.jl</a>–&gt;</p><ul><li><a href="https://github.com/QuantumSavory/QuantumClifford.jl">QuantumClifford.jl</a></li></ul><p>&lt;!–- <a href="https://github.com/iitis/QuantumInformation.jl">QuantumInformation.jl</a> (abandoned)–&gt;</p><ul><li><a href="https://github.com/qojulia/QuantumOptics.jl">QuantumOptics.jl</a></li><li><a href="https://github.com/qutip/QuantumToolbox.jl">QuantumToolbox.jl</a></li><li><a href="https://github.com/QuantumBFS/Yao.jl">Yao.jl</a></li></ul><p>Python: &lt;!–- <a href="https://github.com/qutip/qutip">qutip</a>–&gt; &lt;!–- <a href="https://github.com/qutip/qutip-qip">qutip-qip</a>–&gt;</p><ul><li><a href="https://github.com/vprusso/toqito">toqito</a></li></ul><p>MATLAB:</p><ul><li><a href="https://github.com/nathanieljohnston/QETLAB">QETLAB</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="api/">List of functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 16 January 2025 07:11">Thursday 16 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · Ket.jl</title><meta name="title" content="Home · Ket.jl"/><meta property="og:title" content="Home · Ket.jl"/><meta property="twitter:title" content="Home · Ket.jl"/><meta name="description" content="Documentation for Ket.jl."/><meta property="og:description" content="Documentation for Ket.jl."/><meta property="twitter:description" content="Documentation for Ket.jl."/><meta property="og:url" content="https://dev-ket.github.io/Ket.jl/"/><meta property="twitter:url" content="https://dev-ket.github.io/Ket.jl/"/><link rel="canonical" href="https://dev-ket.github.io/Ket.jl/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="search_index.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-mocha.css" data-theme-name="catppuccin-mocha"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-macchiato.css" data-theme-name="catppuccin-macchiato"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-frappe.css" data-theme-name="catppuccin-frappe"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/catppuccin-latte.css" data-theme-name="catppuccin-latte"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href><img class="docs-light-only" src="assets/logo.svg" alt="Ket.jl logo"/><img class="docs-dark-only" src="assets/logo-dark.svg" alt="Ket.jl logo"/></a><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Installation"><span>Installation</span></a></li><li><a class="tocitem" href="#Related-libraries"><span>Related libraries</span></a></li></ul></li><li><a class="tocitem" href="api/">List of functions</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/dev-ket/Ket.jl/blob/master/README.md" title="View source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p><a href="https://dev-ket.github.io/Ket.jl/dev/"><img src="https://dev-ket.github.io/Ket.jl/dev/assets/ket-jl-logo-dark-wide.svg" alt="Banner"/></a></p><p><a href="https://dev-ket.github.io/Ket.jl/dev/"><img src="https://img.shields.io/badge/docs-dev-blue.svg" alt="Dev"/></a></p><p>Ket is a toolbox for quantum information, nonlocality, and entanglement written in the Julia programming language. All its functions are designed to work with generic types, allowing one to use <code>Int64</code> or <code>Float64</code> for efficiency, or arbitrary precision types when needed. Wherever possible they can be also used for optimization with <a href="https://jump.dev/JuMP.jl/stable/">JuMP</a>. And everything is optimized to the last microsecond.</p><p>Highlights:</p><ul><li>Work with multipartite Bell inequalities, computing their local bounds and Tsirelson bounds with <code>local_bound</code> and <code>tsirelson_bound</code>, and transforming between Collins-Gisin, probability, and correlator representations with <code>tensor_collinsgisin</code>, <code>tensor_probability</code>, and <code>tensor_correlation</code>.</li><li>Work with bipartite entanglement by computing the relative entropy of entanglement, random robustness, or Schmidt number via <code>entanglement_entropy</code>, <code>random_robustness</code>, and <code>schmidt_number</code>. Under the hood these functions use the DPS hierarchy, which is also available in isolation via <code>_dps_constraints!</code>.</li><li>Generate MUBs and SIC-POVMs through <code>mub</code> and <code>sic_povm</code>.</li><li>Generate uniformly-distributed random states, unitaries, and POVMs with <code>random_state</code>, <code>random_unitary</code>, and <code>random_povm</code>.</li><li>Generate well-known families of quantum states, such as the Bell states, the GHZ state, the W state, and the super-singlet via <code>state_bell</code>, <code>state_ghz</code>, <code>state_w</code>, and <code>state_supersinglet</code>.</li><li>Work with multilinear algebra via utility functions such as <code>partial_trace</code>, <code>partial_transpose</code>, and <code>permute_systems</code>.</li><li>Generate kets with <code>ket</code>.</li></ul><p>For the full list of functions see the <a href="https://dev-ket.github.io/Ket.jl/dev/api/">documentation</a>.</p><h2 id="Installation"><a class="docs-heading-anchor" href="#Installation">Installation</a><a id="Installation-1"></a><a class="docs-heading-anchor-permalink" href="#Installation" title="Permalink"></a></h2><p>Ket is a registered Julia package, so it can be installed by typing</p><pre><code class="nohighlight hljs">]add Ket</code></pre><p>into the Julia REPL.</p><h2 id="Related-libraries"><a class="docs-heading-anchor" href="#Related-libraries">Related libraries</a><a id="Related-libraries-1"></a><a class="docs-heading-anchor-permalink" href="#Related-libraries" title="Permalink"></a></h2><p>Julia: &lt;!–- <a href="https://github.com/ZIB-IOL/BellPolytopes.jl">BellPolytopes.jl</a>–&gt;</p><ul><li><a href="https://github.com/QuantumSavory/QuantumClifford.jl">QuantumClifford.jl</a></li></ul><p>&lt;!–- <a href="https://github.com/iitis/QuantumInformation.jl">QuantumInformation.jl</a> (abandoned)–&gt;</p><ul><li><a href="https://github.com/qojulia/QuantumOptics.jl">QuantumOptics.jl</a></li><li><a href="https://github.com/qutip/QuantumToolbox.jl">QuantumToolbox.jl</a></li><li><a href="https://github.com/QuantumBFS/Yao.jl">Yao.jl</a></li></ul><p>Python: &lt;!–- <a href="https://github.com/qutip/qutip">qutip</a>–&gt; &lt;!–- <a href="https://github.com/qutip/qutip-qip">qutip-qip</a>–&gt;</p><ul><li><a href="https://github.com/vprusso/toqito">toqito</a></li></ul><p>MATLAB:</p><ul><li><a href="https://github.com/nathanieljohnston/QETLAB">QETLAB</a></li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="api/">List of functions »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Thursday 16 January 2025 09:48">Thursday 16 January 2025</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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