CINXE.COM

<!DOCTYPE html><html xml:lang="en" lang="en"><head><title>Fundamentals of Quantum Entanglement (Second Edition) - Book - IOPscience</title><meta charset="utf-8" /><meta http-equiv="x-ua-compatible" content="IE=edge" /><meta name="viewport" content="width=device-width, initial-scale=1.0, minimum-scale=1.0" /><script> function DeferJS(src) { function downloadJSAtOnload() { var element = document.createElement("script"); element.src = src; document.body.appendChild(element); } if (window.addEventListener) window.addEventListener("load", downloadJSAtOnload, false); else if (window.attachEvent) window.attachEvent("onload", downloadJSAtOnload); else window.onload = downloadJSAtOnload; } </script><meta name="citation_title" content="Fundamentals of Quantum Entanglement (Second Edition)"></meta><meta name="citation_author" content="F J Duarte"></meta><meta name="citation_publication_date" content="2022/09/01"></meta><meta name="citation_publisher" content="IOP Publishing"></meta><meta name="citation_isbn" content="978-0-7503-5269-7"></meta><meta name="citation_pdf_url" content="https://iopscience.iop.org/book/mono/978-0-7503-5269-7.preview.pdf"></meta><meta name="citation_xml_url" content="https://iopscience.iop.org/book/mono/978-0-7503-5269-7/xml"></meta><meta name="citation_abstract" content="<p>Quantum entanglement (QE) has rapidly become a subject of great interest in academia, industry, and government research institutions. This book builds on the first edition of Fundamentals of Quantum Entanglement to provide a transparent and more insightful introduction for graduate students, scientists, and engineers. It is also a highly useful education tool for those practitioners that were not aware of the physical origin of quantum entanglement: the Dirac—Wheeler—Pryce—Ward physics. The new edition includes an expansion on topics such as quantum entropy and quantum time. The book provides a direct, practical, and transparent introduction to the principles and physics of quantum entanglement. It does so whilst utilizing an interferometric approach based on Dirac—Feynman superposition probability amplitudes. Part of <a href="https://iopscience.iop.org/bookListInfo/series-in-coherent-sources-and-applications#series">IOP Series in Coherent Sources, Quantum Fundamentals, and Applications</a>.</p><p>Key features</p><p>• Provides an overview of quantum entanglement at a basic level</p><p>• Explains the philosophical origin of quantum entanglement as well as the physical origin</p><p>• Presents the key equation for the probability amplitude for QE from three perspectives while emphasizing its interferometric derivation</p><p>• Includes applications on Quantum Cryptography, Quantum Teleportation, Quantum Computing</p><p>• Reviews the current technology of QE with an emphasis in space-to-space communications</p>"></meta><meta name="asset_id" content="10__1088_978-0-7503-5269-7"></meta><meta name="asset_type" content="book"></meta><script type="text/javascript"> //start common.config (function () { let config = {"SHOW_REFERENCE_ENTITLEMENT":"false","SECURED_ENVIRONMENT":"true","ENABLE_MATHJAX_BY_DEFAULT":"true"} || {}; window.config = {...config, ...window.config}; })(); //end common.config </script><script> var _urconfig = { sid: "defc3a7d-4b34-4b6f-ad1c-0716e0a05a65", aip: 0, usePageProtocol: false }; (function (d, s) { var js = d.createElement(s), sc = d.getElementsByTagName(s)[0]; js.src = "https://hit.uptrendsdata.com/rum.min.js"; js.async = "async"; sc.parentNode.insertBefore(js, sc); } (document, "script")); </script><meta name="robots" content="noarchive" /><link rel="stylesheet" href="https://static.iopscience.com/3.80.1/css/critical-styles.min.css" type="text/css"/><link rel="stylesheet" href="https://static.iopscience.com/3.80.1/css/main-styles.min.css" media="print" onload="this.media='all'"/><script> window.iabConfig = { allowedVendors: ['755','804', '1020'], allowedGoogleVendors: [] } </script><script type="text/javascript"> (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', 'GTM-M73Z4W'); </script><script> const mathjaxVersion = 3; </script><script async src="https://securepubads.g.doubleclick.net/tag/js/gpt.js"></script><script> window.googletag = window.googletag || {cmd: []}; googletag.cmd.push(function () { const leaderboard = googletag.sizeMapping().addSize([800, 0], [728, 90]).addSize([640, 690], [180, 150]).addSize([0, 0], [180, 150]).build(); googletag.defineSlot('/21821800277/iopsc/iopsc_m_hp_ap', new Array([728, 90], [300, 250], [180, 150]), 'div-gpt-ad-1562594774007-0').defineSizeMapping(leaderboard).addService(googletag.pubads()); googletag.defineSlot('/21821800277/iopsc/iopsc_x11_hp_ap', [180, 150], 'div-gpt-ad-1562595009103-0').addService(googletag.pubads()); googletag.defineSlot('/21821800277/iopsc/iopsc_pubgrade1_ap', [160, 600], 'div-gpt-ad-1665567578228-0').addService(googletag.pubads()); const googleLeaderboardMapping = googletag.sizeMapping() .addSize([1000, 0], [970, 90]) .addSize([350, 0], [320, 50]) .addSize([0, 0], []) .build(); googletag.defineSlot('/21821800277/iopsc/iopsc_top_hp_ap', new Array([970, 90], [320, 50]), 'div-gpt-ad-1709814088027-0') .defineSizeMapping(googleLeaderboardMapping) .addService(googletag.pubads()); const googleSkyscraperMapping = googletag.sizeMapping().addSize([800, 0], [160, 600]).addSize([350, 250], [300, 250]).addSize([0, 0], []).build(); googletag.defineSlot('/21821800277/iopsc/iopsc_skyscraper1_hp_ap', new Array([160, 600], [300, 250]), 'div-gpt-ad-1669279847892-0').defineSizeMapping(googleSkyscraperMapping).addService(googletag.pubads()); const tagArray = "".split(","); googletag.pubads().enableSingleRequest(); googletag.pubads() .setTargeting("article_tag", tagArray) .setTargeting("pagetype", "book") .setTargeting("iopscience_issn", "") .setTargeting("iopscience_vol", "") .setTargeting("iopscience_issue", "") .setTargeting("iopscience_doi", "10__1088_978-0-7503-5269-7") .setTargeting("iopscience_isbn", "978-0-7503-5269-7") .setTargeting("iopscience_chapter_no", ""); // seting page level targeting googletag.pubads().enableSingleRequest(); googletag.pubads().collapseEmptyDivs(); googletag.enableServices(); }); </script><script> DeferJS("https://d1bxh8uas1mnw7.cloudfront.net/assets/embed.js"); </script><script> DeferJS("https://badge.dimensions.ai/badge.js"); </script><script>var __uzdbm_1 = "1f65d720-928c-4e66-acac-0f73ac9e6cfa";var __uzdbm_2 = "MWJhZjlhOTctY252ai00MjM1LThiMjgtYjU3ODk0NjI4Yzc5JDguMjIyLjIwOC4xNDY=";var __uzdbm_3 = "7f600026e58d84-3f1b-4996-8ea2-8137a75ee16617397733335870-adc32ad778ec86ee10";var __uzdbm_4 = "false";var __uzdbm_5 = "uzmx";var __uzdbm_6 = "7f90002daa83ff-7aa0-4638-b368-29970c4a60cc1-17397733335870-212c6333ec39702e10";var __uzdbm_7 = "iop.org";</script> <script> (function (w, d, e, u, c, g, a, b) { w["SSJSConnectorObj"] = w["SSJSConnectorObj"] || { ss_cid: c, domain_info: "auto", }; w[g] = function (i, j) { w["SSJSConnectorObj"][i] = j; }; a = d.createElement(e); a.async = true; if ( navigator.userAgent.indexOf('MSIE') !== -1 || navigator.appVersion.indexOf('Trident/') > -1 ) { u = u.replace("/advanced/", "/advanced/ie/"); } a.src = u; b = d.getElementsByTagName(e)[0]; b.parentNode.insertBefore(a, b); })( window, document, "script", "https://iopscience.iop.org/18f5227b-e27b-445a-a53f-f845fbe69b40/stormcaster.js", "cnvl", "ssConf" ); ssConf("c1", "https://iopscience.iop.org"); ssConf("c3", "c99a4269-161c-4242-a3f0-28d44fa6ce24"); ssConf("au", "iopscience.iop.org"); ssConf("cu", "validate.perfdrive.com, ssc"); </script></head><body itemscope itemtype="http://schema.org/Organization"><a id="back-to-top-target" tabindex="-1"></a><noscript><iframe title="GA" src="https://www.googletagmanager.com/ns.html?id=GTM-M73Z4W" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript><div class="content-grid"><header class="content-grid__full-width" role="banner" data-nav-group><a class="sr-skip sr-skip--overlay header__skip" href="#skip-to-content-link-target">Skip to content</a><div class="accessibility" style="display: none;"><p><strong>Accessibility Links</strong></p><ul><li><a href="#page-content">Skip to content</a></li><li><a href="/search#contentCol">Skip to search IOPscience</a></li><li><a href="/journals#contentCol">Skip to Journals list</a></li><li><a href="/page/accessibility#contentCol">Accessibility help</a></li></ul></div><div class="dgh-showgrid tgh-showgrid cf" name="contentCol"><nav role="navigation" class="wd-main-nav" aria-label="Site"><a href="#sidr-main" id="simple-menu" class="nav-top-link" aria-label="Menu"><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512"><path d="M0 96C0 78.3 14.3 64 32 64H416c17.7 0 32 14.3 32 32s-14.3 32-32 32H32C14.3 128 0 113.7 0 96zM0 256c0-17.7 14.3-32 32-32H416c17.7 0 32 14.3 32 32s-14.3 32-32 32H32c-17.7 0-32-14.3-32-32zM448 416c0 17.7-14.3 32-32 32H32c-17.7 0-32-14.3-32-32s14.3-32 32-32H416c17.7 0 32 14.3 32 32z"/></svg></a><a href="/" itemprop="url" class="header-logo wd-header-graphic"><meta itemprop="name" content="IOPscience"><img height="15" width="100" src="data:image/svg+xml;base64,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" alt=""><span class="offscreen-hidden">IOP Science home</span></a><a class="btn btn-default" id="accessibility-help" href="/page/accessibility">Accessibility Help</a><ul id="sidr" class="nav__list"><li class="nav-search nav-item"><button class="nav-top-link-drop-down nav-top-link-drop-down--icon" data-nav-trigger="articlelookup"><svg class="fa-icon fa-icon--lrg" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><title>Search</title><path d="M416 208c0 45.9-14.9 88.3-40 122.7L502.6 457.4c12.5 12.5 12.5 32.8 0 45.3s-32.8 12.5-45.3 0L330.7 376c-34.4 25.2-76.8 40-122.7 40C93.1 416 0 322.9 0 208S93.1 0 208 0S416 93.1 416 208zM208 352a144 144 0 1 0 0-288 144 144 0 1 0 0 288z"/></svg></button><div class="nav-drop-down nav-drop-down--full-width" data-nav-item="articlelookup"><div class="wrapper--search cf"><div id="search" class="wd-header-search art-lookup__search"><form accept-charset="utf-8,iso-8859-1" class="primary-search" method="get" action="/nsearch" role="search"><div class="art-lookup__fields-wrapper"><label for="quickSearch">Search all IOPscience content</label><input type="search" x-webkit-speech="" name="terms" id="quickSearch" class="art-lookup__field--grow" placeholder="Search all IOPscience content" value="" escapeXml="true"/><button type="submit" x-webkit-speech="" class="btn btn-default hdr-search-btn bd-0 art-lookup__submit">Search</button></div></form></div><div id="wd-content-finder" class="art-lookup__content-finder"><form accept-charset="utf-8,iso-8859-1" method="get" action="/findcontent" name="contentFinderForm" id="wd-find-art-form" class="find-article-issue-display" autocomplete="OFF" aria-labelledby="article-lookup"><fieldset><legend id="article-lookup" class="eyebrow eyebrow--blue">Article Lookup</legend><div class="art-lookup__fields-wrapper"><label for="CF_JOURNAL" class="offscreen-hidden">Select journal (required)</label><select name="CF_JOURNAL" class="find-article-select art-lookup__content-finder-field art-lookup__field--grow art-lookup__content-finder-field--first" id="CF_JOURNAL"><option value="none" selected="selected">Select journal (required)</option><option value="2053-1583">2D Mater. (2014 - present)</option><option value="1004-423X">Acta Phys. Sin. (Overseas Edn) (1992 - 1999)</option><option value="2043-6262">Adv. Nat. Sci: Nanosci. Nanotechnol. (2010 - present)</option><option value="1882-0786">Appl. Phys. Express (2008 - present)</option><option value="1758-5090">Biofabrication (2009 - present)</option><option value="1748-3190">Bioinspir. Biomim. (2006 - present)</option><option value="1748-605X">Biomed. Mater. (2006 - present)</option><option value="2057-1976">Biomed. Phys. Eng. Express (2015 - present)</option><option value="0508-3443">Br. J. Appl. Phys. (1950 - 1967)</option><option value="1009-9271">Chin. J. Astron. Astrophys. (2001 - 2008)</option><option value="1003-7713">Chin. J. Chem. Phys. (1987 - 2007)</option><option value="1674-0068">Chin. J. Chem. Phys. (2008 - 2012)</option><option value="1009-1963">Chinese Phys. (2000 - 2007)</option><option value="1674-1056">Chinese Phys. B (2008 - present)</option><option value="1674-1137">Chinese Phys. C (2008 - present)</option><option value="0256-307X">Chinese Phys. Lett. (1984 - present)</option><option value="0264-9381">Class. Quantum Grav. (1984 - present)</option><option value="0143-0815">Clin. Phys. Physiol. Meas. (1980 - 1992)</option><option value="1364-7830">Combustion Theory and Modelling (1997 - 2004)</option><option value="0253-6102">Commun. Theor. Phys. (1982 - present)</option><option value="1749-4699">Comput. Sci. Discov. (2008 - 2015)</option><option value="2057-1739">Converg. Sci. Phys. Oncol. (2015 - 2018)</option><option value="0967-1846">Distrib. Syst. Engng. (1993 - 1999)</option><option value="2754-2734">ECS Adv. (2022 - present)</option><option value="2162-8734">ECS Electrochem. Lett. (2012 - 2015)</option><option value="2162-8777">ECS J. Solid State Sci. Technol. (2012 - present)</option><option value="2754-2726">ECS Sens. Plus (2022 - present)</option><option value="2162-8750">ECS Solid State Lett. (2012 - 2015)</option><option value="1938-5862">ECS Trans. (2005 - 2024)</option><option value="0295-5075">EPL (1986 - present)</option><option value="1944-8783">Electrochem. Soc. Interface (1992 - present)</option><option value="1944-8775">Electrochem. Solid-State Lett. (1998 - 2012)</option><option value="2516-1075">Electron. Struct. (2019 - present)</option><option value="2631-8695">Eng. Res. Express (2019 - present)</option><option value="2515-7620">Environ. Res. Commun. (2018 - present)</option><option value="1748-9326">Environ. Res. Lett. (2006 - present)</option><option value="2752-5295">Environ. Res.: Climate (2022 - present)</option><option value="2752-664X">Environ. Res.: Ecology (2022 - present)</option><option value="2753-3751">Environ. Res.: Energy (2024 - present)</option><option value="2976-601X">Environ. Res.: Food Syst. (2024 - present)</option><option value="2752-5309">Environ. Res.: Health (2022 - present)</option><option value="2634-4505">Environ. Res.: Infrastruct. Sustain. (2021 - present)</option><option value="3033-4942">Environ. Res.: Water (2025 - present)</option><option value="0143-0807">Eur. J. Phys. (1980 - present)</option><option value="2058-8585">Flex. Print. Electron. (2015 - present)</option><option value="1873-7005">Fluid Dyn. Res. (1986 - present)</option><option value="2631-6331">Funct. Compos. Struct. (2018 - present)</option><option value="1755-1315">IOP Conf. Ser.: Earth Environ. Sci. (2008 - present)</option><option value="1757-899X">IOP Conf. Ser.: Mater. Sci. Eng. (2009 - present)</option><option value="2633-1357">IOPSciNotes (2020 - 2022)</option><option value="2631-7990">Int. J. Extrem. Manuf. (2019 - present)</option><option value="0266-5611">Inverse Problems (1985 - present)</option><option value="1064-5632">Izv. Math. (1993 - present)</option><option value="1752-7163">J. Breath Res. (2007 - present)</option><option value="1475-7516">J. Cosmol. Astropart. Phys. (2003 - present)</option><option value="1945-7111">J. Electrochem. Soc. (1902 - present)</option><option value="1742-2140">J. Geophys. Eng. (2004 - 2018)</option><option value="1126-6708">J. High Energy Phys. (1997 - 2009)</option><option value="1748-0221">J. Inst. (2006 - present)</option><option value="0960-1317">J. Micromech. Microeng. (1991 - present)</option><option value="1741-2552">J. Neural Eng. (2004 - present)</option><option value="0368-3281">J. Nucl. Energy, Part C Plasma Phys. (1959 - 1966)</option><option value="0150-536X">J. Opt. (1977 - 1998)</option><option value="2040-8986">J. Opt. (2010 - present)</option><option value="1464-4258">J. Opt. A: Pure Appl. Opt. (1999 - 2009)</option><option value="1464-4266">J. Opt. B: Quantum Semiclass. Opt. (1999 - 2005)</option><option value="0022-3689">J. Phys. A: Gen. Phys. (1968 - 1972)</option><option value="0305-4470">J. Phys. A: Math. Gen. (1975 - 2006)</option><option value="0301-0015">J. Phys. A: Math. Nucl. Gen. (1973 - 1974)</option><option value="1751-8121">J. Phys. A: Math. Theor. (2007 - present)</option><option value="0953-4075">J. Phys. B: At. Mol. Opt. Phys. (1988 - present)</option><option value="0022-3700">J. Phys. B: Atom. Mol. Phys. (1968 - 1987)</option><option value="0022-3719">J. Phys. C: Solid State Phys. (1968 - 1988)</option><option value="2399-6528">J. Phys. Commun. (2017 - present)</option><option value="2632-072X">J. Phys. Complex. (2019 - present)</option><option value="0022-3727">J. Phys. D: Appl. Phys. (1968 - present)</option><option value="0022-3735">J. Phys. E: Sci. Instrum. (1968 - 1989)</option><option value="2515-7655">J. Phys. Energy (2018 - present)</option><option value="0305-4608">J. Phys. F: Met. Phys. (1971 - 1988)</option><option value="0954-3899">J. Phys. G: Nucl. Part. Phys. (1989 - present)</option><option value="0305-4616">J. Phys. G: Nucl. Phys. (1975 - 1988)</option><option value="2515-7639">J. Phys. Mater. (2018 - present)</option><option value="2515-7647">J. Phys. Photonics (2018 - present)</option><option value="0953-8984">J. Phys.: Condens. Matter (1989 - present)</option><option value="1742-6596">J. Phys.: Conf. Ser. (2004 - present)</option><option value="0952-4746">J. Radiol. Prot. (1988 - present)</option><option value="3050-2454">J. Reliab. Sci. Eng. (2025 - present)</option><option value="0950-7671">J. Sci. Instrum. (1923 - 1967)</option><option value="1674-4926">J. Semicond. (2009 - present)</option><option value="0260-2814">J. Soc. Radiol. Prot. (1981 - 1987)</option><option value="1742-5468">J. Stat. Mech. (2004 - present)</option><option value="1468-5248">JoT (2000 - 2004)</option><option value="1347-4065">Jpn. J. Appl. Phys. (1962 - present)</option><option value="1555-6611">Laser Phys. (2013 - present)</option><option value="1612-202X">Laser Phys. Lett. (2004 - present)</option><option value="3049-4753">Mach. Learn.: Earth (2025 - present)</option><option value="3049-4761">Mach. Learn.: Eng. (2025 - present)</option><option value="3049-477X">Mach. Learn.: Health (2025 - present)</option><option value="2632-2153">Mach. Learn.: Sci. Technol. (2019 - present)</option><option value="2752-5724">Mater. Futures (2022 - present)</option><option value="2633-4356">Mater. Quantum. Technol. (2020 - present)</option><option value="2053-1591">Mater. Res. Express (2014 - present)</option><option value="0025-5726">Math. USSR Izv. (1967 - 1992)</option><option value="0025-5734">Math. USSR Sb. (1967 - 1993)</option><option value="0957-0233">Meas. Sci. Technol. (1990 - present)</option><option value="2151-2043">Meet. Abstr. (2002 - present)</option><option value="2050-6120">Methods Appl. Fluoresc. (2013 - present)</option><option value="0026-1394">Metrologia (1965 - present)</option><option value="0965-0393">Modelling Simul. Mater. Sci. Eng. (1992 - present)</option><option value="2399-7532">Multifunct. Mater. (2018 - 2022)</option><option value="2632-959X">Nano Ex. (2020 - present)</option><option value="2399-1984">Nano Futures (2017 - present)</option><option value="0957-4484">Nanotechnology (1990 - present)</option><option value="0954-898X">Network (1990 - 2004)</option><option value="2634-4386">Neuromorph. Comput. Eng. (2021 - present)</option><option value="1367-2630">New J. Phys. (1998 - present)</option><option value="0951-7715">Nonlinearity (1988 - present)</option><option value="0335-7368">Nouvelle Revue d'Optique (1973 - 1976)</option><option value="0029-4780">Nouvelle Revue d'Optique Appliquée (1970 - 1972)</option><option value="0029-5515">Nucl. Fusion (1960 - present)</option><option value="1538-3873">PASP (1889 - present)</option><option value="1478-3975">Phys. Biol. (2004 - present)</option><option value="0031-9112">Phys. Bull. (1950 - 1988)</option><option value="0031-9120">Phys. Educ. (1966 - present)</option><option value="0031-9155">Phys. Med. Biol. (1956 - present)</option><option value="1402-4896">Phys. Scr. (1970 - present)</option><option value="2058-7058">Phys. World (1988 - present)</option><option value="1063-7869">Phys.-Usp. (1993 - present)</option><option value="0305-4624">Physics in Technology (1973 - 1988)</option><option value="0967-3334">Physiol. Meas. (1993 - present)</option><option value="0741-3335">Plasma Phys. Control. Fusion (1984 - present)</option><option value="0032-1028">Plasma Physics (1967 - 1983)</option><option value="2516-1067">Plasma Res. Express (2018 - 2022)</option><option value="1009-0630">Plasma Sci. Technol. (1999 - present)</option><option value="0963-0252">Plasma Sources Sci. Technol. (1992 - present)</option><option value="0959-5309">Proc. Phys. Soc. (1926 - 1948)</option><option value="0370-1328">Proc. Phys. Soc. (1958 - 1967)</option><option value="0370-1298">Proc. Phys. Soc. A (1949 - 1957)</option><option value="0370-1301">Proc. Phys. Soc. B (1949 - 1957)</option><option value="1478-7814">Proc. Phys. Soc. London (1874 - 1925)</option><option value="2576-1579">Proc. Vol. (1967 - 2005)</option><option value="2516-1091">Prog. Biomed. Eng. (2018 - present)</option><option value="2516-1083">Prog. Energy (2018 - present)</option><option value="0963-6625">Public Understand. Sci. (1992 - 2002)</option><option value="0963-9659">Pure Appl. Opt. (1992 - 1998)</option><option value="1469-7688">Quantitative Finance (2001 - 2004)</option><option value="1063-7818">Quantum Electron. (1993 - present)</option><option value="0954-8998">Quantum Opt. (1989 - 1994)</option><option value="2058-9565">Quantum Sci. Technol. (2015 - present)</option><option value="1355-5111">Quantum Semiclass. Opt. (1995 - 1998)</option><option value="0034-4885">Rep. Prog. Phys. (1934 - present)</option><option value="1674-4527">Res. Astron. Astrophys. (2009 - present)</option><option value="2515-5172">Research Notes of the AAS (2017 - present)</option><option value="0034-6683">RevPhysTech (1970 - 1972)</option><option value="0036-021X">Russ. Chem. Rev. (1960 - present)</option><option value="0036-0279">Russ. Math. Surv. (1960 - present)</option><option value="1064-5616">Sb. Math. (1993 - present)</option><option value="1468-6996">Sci. Technol. Adv. Mater. (2000 - 2015)</option><option value="0268-1242">Semicond. Sci. Technol. (1986 - present)</option><option value="0964-1726">Smart Mater. Struct. (1992 - present)</option><option value="0049-1748">Sov. J. Quantum Electron. (1971 - 1992)</option><option value="0038-5670">Sov. Phys. Usp. (1958 - 1992)</option><option value="0953-2048">Supercond. Sci. Technol. (1988 - present)</option><option value="2051-672X">Surf. Topogr.: Metrol. Prop. (2013 - present)</option><option value="2977-3504">Sustain. Sci. Technol. (2024 - present)</option><option value="1538-3881">The Astronomical Journal (1849 - present)</option><option value="0004-637X">The Astrophysical Journal (1996 - present)</option><option value="2041-8205">The Astrophysical Journal Letters (2010 - present)</option><option value="0067-0049">The Astrophysical Journal Supplement Series (1996 - present)</option><option value="2632-3338">The Planetary Science Journal (2020 - present)</option><option value="2156-7395">Trans. Amer: Electrochem. Soc. (1930 - 1930)</option><option value="1945-6859">Trans. Electrochem. Soc. (1931 - 1948)</option><option value="1475-4878">Trans. Opt. Soc. (1899 - 1932)</option><option value="2053-1613">Transl. Mater. Res. (2014 - 2018)</option><option value="0959-7174">Waves Random Media (1991 - 2004)</option></select><label for="CF_VOLUME" class="offscreen-hidden">Volume number:</label><input type="text" name="CF_VOLUME" id="CF_VOLUME" class="art-lookup__content-finder-field" placeholder="Volume" x-webkit-speech=""><label for="CF_ISSUE" class="offscreen-hidden">Issue number (if known):</label><input type="text" name="CF_ISSUE" id="CF_ISSUE" class="art-lookup__content-finder-field" placeholder="Issue" x-webkit-speech=""><label for="CF_PAGE" class="offscreen-hidden">Article or page number:</label><input type="text" name="CF_PAGE" id="CF_PAGE" class="art-lookup__content-finder-field art-lookup__content-finder-field--last" placeholder="Article or page" x-webkit-speech=""><button type="submit" class="btn btn-default art-lookup__submit" name="submit">Lookup</button></div></fieldset></form></div></div></div></li><li class="nav-journals nav-item wd-nav-journal"><button class="nav-top-link-drop-down" data-nav-trigger="journals">Journals<svg aria-hidden="true" class="fa-icon fa-icon--right fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg></button><div class="nav-drop-down wd-nav-journal-dd" data-nav-item="journals"><div class="nav-drop-down__grid"><div class="nav-drop-down__item"><a class="nav-drop-down__item-title" href="/journals" data-ga-event="global-nav-item">Journals list</a><span class="nav-drop-down__item-info m-hide">Browse more than 100 science journal titles</span></div><div class="nav-drop-down__item"><a class="nav-drop-down__item-title" href="/page/subjects" data-ga-event="global-nav-item">Subject collections</a><span class="nav-drop-down__item-info m-hide">Read the very best research published in IOP journals</span></div><div class="nav-drop-down__item"><a class="nav-drop-down__item-title" href="/journals?type=partner#js-tab-pubpart" data-ga-event="global-nav-item">Publishing partners</a><span class="nav-drop-down__item-info m-hide">Partner organisations and publications</span></div><div class="nav-drop-down__item"><a class="nav-drop-down__item-title" href="/info/page/openaccess" data-ga-event="global-nav-item">Open access</a><span class="nav-drop-down__item-info m-hide">IOP Publishing open access policy guide</span></div><div class="nav-drop-down__item"><a class="nav-drop-down__item-title" href="/conference-series" data-ga-event="global-nav-item">IOP Conference Series</a><span class="nav-drop-down__item-info m-hide">Read open access proceedings from science conferences worldwide</span></div></div></div></li><li class="nav-books nav-item wd-nav-books"><a href="/booklistinfo/home" class="nav-top-link">Books</a></li><li class="nav-publishing-support nav-item wd-publishing-support"><a href="https://publishingsupport.iopscience.iop.org" class="nav-top-link" data-ga-event="global-nav-item">Publishing Support</a></li><li class="nav-login nav-item wd-nav-login"><button class="nav-top-link-drop-down" id="login-drop-down-user" data-nav-trigger="login"><svg aria-hidden="true" class="fa-icon fa-icon--left" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M399 384.2C376.9 345.8 335.4 320 288 320H224c-47.4 0-88.9 25.8-111 64.2c35.2 39.2 86.2 63.8 143 63.8s107.8-24.7 143-63.8zM0 256a256 256 0 1 1 512 0A256 256 0 1 1 0 256zm256 16a72 72 0 1 0 0-144 72 72 0 1 0 0 144z"/></svg>Login<svg aria-hidden="true" class="fa-icon fa-icon--right fa-icon--flip" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M137.4 374.6c12.5 12.5 32.8 12.5 45.3 0l128-128c9.2-9.2 11.9-22.9 6.9-34.9s-16.6-19.8-29.6-19.8L32 192c-12.9 0-24.6 7.8-29.6 19.8s-2.2 25.7 6.9 34.9l128 128z"/></svg></button><div class="nav-drop-down wd-nav-login-dd" data-nav-item="login"><a href="https://myiopscience.iop.org/signin?origin=a0&return=https%3A%2F%2Fiopscience.iop.org%2Fbook%2Fmono%2F978-0-7503-5269-7" id="wd-login-link" data-ga-event="global-nav-item">IOPscience login / Sign Up</a></div></li></ul></nav></div></header><div class="page-body" itemtype="http://schema.org/Book" id="book"><div class="grid-3-col da-showgrid ta-showgrid cf"><main id="skip-to-content-link-target"><div class="secondary-header cf" id="wd-secondary-header"><div class="unbranded"><div class="publication-name" id="wd-pub-name"><h1 class="publication-title" itemprop="name" itemref="book"><a href="/book/mono/978-0-7503-5269-7" alt="Fundamentals of Quantum Entanglement (Second Edition)"> Fundamentals of Quantum Entanglement (Second Edition) </a></h1></div></div></div><div class="da1-da2" id="page-content" itemscope="" itemtype="http://schema.org/ScholarlyArticle"><div class="da1 ta1 article-head"><div class="media mb-0"><div class="pull-left book-page-cover-w-meta"><div class="book-cover-and-preview"><img width="125" class="book-cover-and-preview__cover" border="0" itemprop="image" id="wd-book-cover-img" src="https://content.cld.iop.org/books/10__1088_978-0-7503-5269-7/revision7/bk978-0-7503-5269-7cover.jpg" alt=""/><div><a href="/book/mono/978-0-7503-5269-7.preview.pdf" class="btn btn-primary book-cover-and-preview__preview" title="Preview">Preview</a></div></div><p><span class="meta-line" itemtype="http://schema.org/Person" itemprop="author" itemscope="" itemref="book" id="wd-book-author"><b>Author</b><br/> <span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span> </span><span class="meta-line" id="wd-book-pub-date"><b>Published</b><br/><span itemprop="datePublished">September 2022</span></span></p></div><div class="media-body"><div class="btn-multi-block mt-0 mb-05"><p class="small mb-05">Download ebook</p><div class="hover-trigger"><a target="_blank" href="/book/mono/978-0-7503-5269-7.pdf" class="btn btn-large btn-primary content-download event_book-download" data-event-action="PDF" id="wd-book-pdf-but" rel="noopener"><span class="icon-file-pdf"></span><span class="offscreen-hidden">Download</span> PDF<span class="offscreen-hidden"> book</span></a></div><div class="hover-trigger"><a target="_blank" href="/book/mono/978-0-7503-5269-7.epub" aria-describedby="epub-description" class="btn btn-large btn-primary content-download dupe-buttons event_book-download" data-event-action="ePub" id="wd-book-epub-but" rel="noopener"><span class="icon-epub"></span><span class="offscreen-hidden">Download</span><span></span> ePub <span></span><span class="offscreen-hidden">book</span></a><div class="epub-label hover-item bd-1"><p id="epub-description" class="small">You need an eReader or compatible software to experience <a href="http://iopscience.iop.org/page/ePub3">the benefits of the ePub3 file format</a>.</p></div></div></c:if><div class="hover-trigger"><a target="_blank" href="/book/mono/978-0-7503-5269-7.mobi" aria-describedby="kindle-description" class="btn btn-large btn-primary content-download event_book-download" data-event-action="Kindle" id="wd-book-mobi-but" rel="noopener"><span class="icon-file-kindle"></span><span class="offscreen-hidden">Download</span> Kindle<span class="offscreen-hidden"> book</span></a><div class="kindle-label hover-item bd-1"><p id="kindle-description" class="small">Download direct to your Kindle device for instant, off-line reading</p></div></div></div><div itemprop="description" id="wd-book-page-intro"> <p>Quantum entanglement (QE) has rapidly become a subject of great interest in academia, industry, and government research institutions. This book builds on the first edition of Fundamentals of Quantum Entanglement to provide a transparent and more insightful introduction for graduate students, scientists, and engineers. It is also a highly useful education tool for those practitioners that were not aware of the physical origin of quantum entanglement: the Dirac—Wheeler—Pryce—Ward physics. The new edition includes an expansion on topics such as quantum entropy and quantum time. The book provides a direct, practical, and transparent introduction to the principles and physics of quantum entanglement. It does so whilst utilizing an interferometric approach based on Dirac—Feynman superposition probability amplitudes. Part of <a href="https://iopscience.iop.org/bookListInfo/series-in-coherent-sources-and-applications#series">IOP Series in Coherent Sources, Quantum Fundamentals, and Applications</a>.</p><p>Key features</p><p>• Provides an overview of quantum entanglement at a basic level</p><p>• Explains the philosophical origin of quantum entanglement as well as the physical origin</p><p>• Presents the key equation for the probability amplitude for QE from three perspectives while emphasizing its interferometric derivation</p><p>• Includes applications on Quantum Cryptography, Quantum Teleportation, Quantum Computing</p><p>• Reviews the current technology of QE with an emphasis in space-to-space communications</p> </div><p class="small"><span itemprop="copyrightHolder" id="wd-book-copyright">Copyright © IOP Publishing Ltd 2022</span><br /><span itemprop="isbn" id="wd-book-online-isbn">Online ISBN: <span id="epubisbn">978-0-7503-5269-7</span></span> • <span itemprop="isbn" id="wd-book-print-isbn">Print ISBN: 978-0-7503-5265-9</span></p></div></div></div><div class="da2 ta2"><div class="print-hide content-tools"><div class="dimensions-altmetric-li"><h2 class="replica-h5 mt-0">Book metrics</h2><span class="__dimensions_badge_embed__ dimensions-embed" data-hide-zero-citations="true" data-ga-event="dimensions" data-style="small_circle" data-doi="10.1088/978-0-7503-5269-7"></span><div data-badge-popover="right" data-badge-type="donut" data-doi="10.1088/978-0-7503-5269-7" data-hide-no-mentions="true" class="altmetric-embed" data-hide-less-than="1"></div><div class="clear-fl"></div></div><div><h2 class="replica-h5 mt-0">Export citation and abstract</h2><span class="btn-multi-block"><a href="/exportAbstract?isbn=978-0-7503-5269-7&exportFormat=iopexport_bib&exportType=abs" class="btn btn-primary wd-btn-cit-abs-bib" aria-label="BibTeX of citation and abstract">BibTeX</a><a href="/exportAbstract?isbn=978-0-7503-5269-7&exportFormat=iopexport_ris&exportType=abs" class="btn btn-primary wd-btn-cit-abs-ris" aria-label="RIS of citation and abstract">RIS</a></span></div><div><h2 class="replica-h5 mt-0">Permissions</h2><p class="wd-jnl-art-get-permisssion print-hide"><a href="https://www.plsclear.com/pages/ClearWizard.aspx?provider=IOP Publishing Limited&id=978-0-7503-5269-7" target="_blank" rel="noopener">Get permission to re-use this book</a></p></div><div id="wd-share-icons"><h2 class="replica-h5 mt-0">Share this book</h2><ul class="share-icon-links"><li id="wd-share-icon-email"><a href="mailto:?subject=Fundamentals of Quantum Entanglement (Second Edition)&body=Fundamentals of Quantum Entanglement (Second Edition) - https://doi.org/10.1088/978-0-7503-5269-7" aria-label="Share this content via email" class="share-icon-links__link replicate-hover"><svg aria-hidden="true" class="fa-icon" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M64 112c-8.8 0-16 7.2-16 16v22.1L220.5 291.7c20.7 17 50.4 17 71.1 0L464 150.1V128c0-8.8-7.2-16-16-16H64zM48 212.2V384c0 8.8 7.2 16 16 16H448c8.8 0 16-7.2 16-16V212.2L322 328.8c-38.4 31.5-93.7 31.5-132 0L48 212.2zM0 128C0 92.7 28.7 64 64 64H448c35.3 0 64 28.7 64 64V384c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V128z"/></svg></a></li><li id="wd-share-icon-facebook"><a href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fdoi.org%2F10.1088%2F978-0-7503-5269-7" target="_blank" rel="noopener" aria-label="Share on Facebook (opens new window)" class="share-icon-links__link replicate-hover"><svg aria-hidden="true" class="fa-icon" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 320 512"><path d="M80 299.3V512H196V299.3h86.5l18-97.8H196V166.9c0-51.7 20.3-71.5 72.7-71.5c16.3 0 29.4 .4 37 1.2V7.9C291.4 4 256.4 0 236.2 0C129.3 0 80 50.5 80 159.4v42.1H14v97.8H80z"/></svg></a></li><li id="wd-share-icon-twitter"><a href="https://twitter.com/share?url=https%3A%2F%2Fdoi.org%2F10.1088%2F978-0-7503-5269-7&text=Fundamentals+of+Quantum+Entanglement+%28Second+Edition%29&via=ioppublishing" target="_blank" rel="noopener" aria-label="Share on Twitter (opens new window)" class="share-icon-links__link replicate-hover"><svg aria-hidden="true" class="fa-icon" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M389.2 48h70.6L305.6 224.2 487 464H345L233.7 318.6 106.5 464H35.8L200.7 275.5 26.8 48H172.4L272.9 180.9 389.2 48zM364.4 421.8h39.1L151.1 88h-42L364.4 421.8z"/></svg></a></li><li id="wd-share-icon-mendeley"><a href="https://www.mendeley.com/import/?doi=10.1088%2F978-0-7503-5269-7" target="_blank" rel="noopener" aria-label="Share on Mendeley (opens new window)" class="share-icon-links__link replicate-hover"><svg aria-hidden="true" class="fa-icon" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 512"><path d="M624.6 325.2c-12.3-12.4-29.7-19.2-48.4-17.2-43.3-1-49.7-34.9-37.5-98.8 22.8-57.5-14.9-131.5-87.4-130.8-77.4 .7-81.7 82-130.9 82-48.1 0-54-81.3-130.9-82-72.9-.8-110.1 73.3-87.4 130.8 12.2 63.9 5.8 97.8-37.5 98.8-21.2-2.3-37 6.5-53 22.5-19.9 19.7-19.3 94.8 42.6 102.6 47.1 5.9 81.6-42.9 61.2-87.8-47.3-103.7 185.9-106.1 146.5-8.2-.1 .1-.2 .2-.3 .4-26.8 42.8 6.8 97.4 58.8 95.2 52.1 2.1 85.4-52.6 58.8-95.2-.1-.2-.2-.3-.3-.4-39.4-97.9 193.8-95.5 146.5 8.2-4.6 10-6.7 21.3-5.7 33 4.9 53.4 68.7 74.1 104.9 35.2 17.8-14.8 23.1-65.6 0-88.3zm-303.9-19.1h-.6c-43.4 0-62.8-37.5-62.8-62.8 0-34.7 28.2-62.8 62.8-62.8h.6c34.7 0 62.8 28.1 62.8 62.8 0 25-19.2 62.8-62.8 62.8z"/></svg></a></li></ul><div class="clear-fl"></div></div><div id="my_print"><h2 class="replica-h5 mt-0">myPrint</h2><img class="horizontal-logo" src='data:image/svg+xml;base64,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' alt="my print"><p class="mb-0" id="wd-short-desc">In order to take advantage of this service, your institution needs to have access to this IOP ebook content.</p><button class="overlay-launch d-b" aria-expanded="false" id="wd-read-more">Read more</button><a href="/page/book-recommendation" title="Recommend to your Librarian" class="d-b" role="button" id="wd-librarian">Recommend to your Librarian</a><span class="overlay-set"><div class="tint-screen"></div><div role="dialog" aria-label="myPrint. Brought to you by your library" aria-modal="true" class="overlay-panel"><button class="close-icon close-overlay" aria-label="Close"><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path d="M256 512A256 256 0 1 0 256 0a256 256 0 1 0 0 512zM175 175c9.4-9.4 24.6-9.4 33.9 0l47 47 47-47c9.4-9.4 24.6-9.4 33.9 0s9.4 24.6 0 33.9l-47 47 47 47c9.4 9.4 9.4 24.6 0 33.9s-24.6 9.4-33.9 0l-47-47-47 47c-9.4 9.4-24.6 9.4-33.9 0s-9.4-24.6 0-33.9l47-47-47-47c-9.4-9.4-9.4-24.6 0-33.9z"/></svg></button><div class="overlay-img"><img class="circular-logo" alt="my print" src='data:image/svg+xml;base64,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'></div><div class="overlay-text"><h2 class="replica-h3">What is myPrint?</h2><p>myPrint is a new service, offering individuals at institutions who have purchased IOP ebooks the chance to buy their own personal print-copy, direct from iopscience.org.</p><p>The offer is available on any book that your institution has purchased electronically, and are priced at <b>£25/$30</b> (exc. Ship and VAT) per copy. The books come in a durable paperback format, with full-colour cover, black & white contents, and monochrome illustrations (where present).</p><p>We work with our trusted distribution partners, NBN International, to supply the books and deliver them straight to your doorstep. What could be simpler!</p><p class="mb-0">For more details on how to take advantage of this service, or to recommend the title to your librarian, please <a href="https://ioppublishing.org/about-us/contact-us/" id="wd-contact-us">Contact us</a> or <a title="Recommend to your Librarian" href="/page/book-recommendation" id="wd-librarian-popup">Recommend to your Librarian</a></p></div></div></span></div></div></div><div class="da1 ta1"><aside aria-label="Main column advert"><div id='div-gpt-ad-1562594774007-0' style='width: 728px; height: 90px; display: block;'><script> googletag.cmd.push(function () { googletag.display('div-gpt-ad-1562594774007-0'); }); </script></div></aside><div class="tabs cf mb-2 mt-1" id="book-tabs"><div role="tablist"><button role="tab" aria-selected="true" aria-controls="book-toc-tab" id="book-toc" class="event_book-tabs"> Table of contents </button><button role="tab" aria-selected="false" aria-controls="book-about-tab" id="book-about" class="event_book-tabs" tabindex="-1"> About Book </button><button role="tab" aria-selected="false" aria-controls="book-authors-tab" id="book-authors" class="event_book-tabs" tabindex="-1"> Author </button><button role="tab" aria-selected="false" aria-controls="book-multimedia-tab" id="book-multimedia" class="event_book-tabs" tabindex="-1"> Supplementary material </button><button role="tab" aria-selected="false" aria-controls="book-review-tab" id="book-review" class="event_book-tabs" tabindex="-1"> Reviews </button></div><div tabindex="0" role="tabpanel" id="book-toc-tab" aria-labelledby="book-toc"><div class="tab-content-padding"><div class="art-list mt-2" id="wd-book-toc"><div class="art-list-item"><div class="art-list-item-body"><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch0.pdf">Front matter</a></h2><div class="art-list-item-tools small"><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch0.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Front matter" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Front matter</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch0.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Front matter"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Front matter</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 1-1 to 1-17</div><span class="eyebrow"><span class="offscreen-hidden">The following chapter is </span><span class="red">Free to read</span></span><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch1">Introduction</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch1" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Introduction"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Introduction</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch1.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Introduction" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Introduction</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch1.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Introduction"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Introduction</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 2-1 to 2-17</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch2">Dirac's physics</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch2" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Dirac’s physics"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Dirac's physics</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch2.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Dirac’s physics" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Dirac's physics</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch2.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Dirac’s physics"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Dirac's physics</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 3-1 to 3-5</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch3">The Einstein–Podolsky–Rosen (EPR) paper</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch3" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The Einstein–Podolsky–Rosen (EPR) paper"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The Einstein–Podolsky–Rosen (EPR) paper</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch3.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The Einstein–Podolsky–Rosen (EPR) paper" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The Einstein–Podolsky–Rosen (EPR) paper</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch3.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The Einstein–Podolsky–Rosen (EPR) paper"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The Einstein–Podolsky–Rosen (EPR) paper</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 4-1 to 4-3</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch4">The Schrödinger papers</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch4" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The Schrödinger papers"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The Schrödinger papers</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch4.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The Schrödinger papers" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The Schrödinger papers</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch4.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The Schrödinger papers"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The Schrödinger papers</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 5-1 to 5-3</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch5">Wheeler's paper</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch5" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Wheeler’s paper"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Wheeler's paper</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch5.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Wheeler’s paper" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Wheeler's paper</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch5.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Wheeler’s paper"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Wheeler's paper</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 6-1 to 6-6</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch6">The probability amplitude for quantum entanglement</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch6" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The probability amplitude for quantum entanglement"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The probability amplitude for quantum entanglement</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch6.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The probability amplitude for quantum entanglement" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The probability amplitude for quantum entanglement</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch6.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The probability amplitude for quantum entanglement"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The probability amplitude for quantum entanglement</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 7-1 to 7-3</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch7">The quantum entanglement experiment</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch7" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The quantum entanglement experiment"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The quantum entanglement experiment</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch7.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The quantum entanglement experiment" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The quantum entanglement experiment</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch7.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The quantum entanglement experiment"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The quantum entanglement experiment</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 8-1 to 8-5</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch8">The annihilation quantum entanglement experiments</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch8" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The annihilation quantum entanglement experiments"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The annihilation quantum entanglement experiments</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch8.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The annihilation quantum entanglement experiments" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The annihilation quantum entanglement experiments</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch8.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The annihilation quantum entanglement experiments"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The annihilation quantum entanglement experiments</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 9-1 to 9-4</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch9">The Bohm and Aharonov paper</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch9" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The Bohm and Aharonov paper"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The Bohm and Aharonov paper</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch9.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The Bohm and Aharonov paper" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The Bohm and Aharonov paper</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch9.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The Bohm and Aharonov paper"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The Bohm and Aharonov paper</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 10-1 to 10-7</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch10">Bell's theorem</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch10" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Bell’s theorem"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Bell's theorem</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch10.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Bell’s theorem" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Bell's theorem</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch10.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Bell’s theorem"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Bell's theorem</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 11-1 to 11-5</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch11">Feynman's Hamiltonians</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch11" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Feynman’s Hamiltonians"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Feynman's Hamiltonians</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch11.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Feynman’s Hamiltonians" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Feynman's Hamiltonians</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch11.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Feynman’s Hamiltonians"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Feynman's Hamiltonians</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 12-1 to 12-4</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch12">The second Wu quantum entanglement experiment</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch12" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The second Wu quantum entanglement experiment"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The second Wu quantum entanglement experiment</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch12.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The second Wu quantum entanglement experiment" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The second Wu quantum entanglement experiment</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch12.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The second Wu quantum entanglement experiment"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The second Wu quantum entanglement experiment</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 13-1 to 13-5</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch13">The hidden variable theory experiments</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch13" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The hidden variable theory experiments"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The hidden variable theory experiments</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch13.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The hidden variable theory experiments" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The hidden variable theory experiments</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch13.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The hidden variable theory experiments"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The hidden variable theory experiments</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 14-1 to 14-7</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch14">The optical quantum entanglement experiments</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch14" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The optical quantum entanglement experiments"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The optical quantum entanglement experiments</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch14.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The optical quantum entanglement experiments" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The optical quantum entanglement experiments</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch14.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The optical quantum entanglement experiments"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The optical quantum entanglement experiments</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 15-1 to 15-5</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch15">The quantum entanglement probability amplitude 1947–1992</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch15" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The quantum entanglement probability amplitude 1947–1992"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The quantum entanglement probability amplitude 1947–1992</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch15.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The quantum entanglement probability amplitude 1947–1992" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The quantum entanglement probability amplitude 1947–1992</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch15.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The quantum entanglement probability amplitude 1947–1992"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The quantum entanglement probability amplitude 1947–1992</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 16-1 to 16-3</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch16">The GHZ probability amplitudes</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch16" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The GHZ probability amplitudes"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The GHZ probability amplitudes</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch16.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The GHZ probability amplitudes" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The GHZ probability amplitudes</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch16.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The GHZ probability amplitudes"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The GHZ probability amplitudes</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 17-1 to 17-6</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch17">The interferometric derivation of the quantum entanglement probability amplitude for <i>n</i> = <i>N</i> = 2</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch17" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch17.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch17.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 18-1 to 18-11</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch18">The interferometric derivation of the quantum entanglement probability amplitude for <i>n</i> = <i>N</i> = 2<sup>1</sup>, 2<sup>2</sup>, 2<sup>3</sup>, 2<sup>4</sup>... 2<sup><i>r</i></sup></a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch18" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24… 2r"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24... 2r</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch18.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24… 2r" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24... 2r</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch18.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24… 2r"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24... 2r</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 19-1 to 19-6</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch19">The interferometric derivation of the quantum entanglement probability amplitudes for <i>n</i> = <i>N</i> = 3, 6</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch19" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch19.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch19.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 20-1 to 20-7</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch20">Quantum entanglement at <i>n</i> = 1 and <i>N</i> = 2</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch20" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum entanglement at n = 1 and N = 2"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum entanglement at n = 1 and N = 2</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch20.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum entanglement at n = 1 and N = 2" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum entanglement at n = 1 and N = 2</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch20.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum entanglement at n = 1 and N = 2"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum entanglement at n = 1 and N = 2</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 21-1 to 21-10</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch21">Quantum entanglement probability amplitudes applied to Bell's theorem</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch21" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum entanglement probability amplitudes applied to Bell’s theorem"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum entanglement probability amplitudes applied to Bell's theorem</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch21.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum entanglement probability amplitudes applied to Bell’s theorem" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum entanglement probability amplitudes applied to Bell's theorem</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch21.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum entanglement probability amplitudes applied to Bell’s theorem"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum entanglement probability amplitudes applied to Bell's theorem</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 22-1 to 22-10</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch22">Quantum entanglement via matrix notation</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch22" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum entanglement via matrix notation"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum entanglement via matrix notation</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch22.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum entanglement via matrix notation" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum entanglement via matrix notation</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch22.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum entanglement via matrix notation"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum entanglement via matrix notation</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 23-1 to 23-8</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch23">Cryptography via quantum entanglement</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch23" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Cryptography via quantum entanglement"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Cryptography via quantum entanglement</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch23.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Cryptography via quantum entanglement" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Cryptography via quantum entanglement</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch23.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Cryptography via quantum entanglement"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Cryptography via quantum entanglement</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 24-1 to 24-6</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch24">Quantum entanglement and teleportation</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch24" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum entanglement and teleportation"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum entanglement and teleportation</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch24.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum entanglement and teleportation" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum entanglement and teleportation</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch24.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum entanglement and teleportation"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum entanglement and teleportation</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 25-1 to 25-13</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch25">Quantum entanglement and quantum computing</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch25" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum entanglement and quantum computing"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum entanglement and quantum computing</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch25.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum entanglement and quantum computing" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum entanglement and quantum computing</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch25.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum entanglement and quantum computing"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum entanglement and quantum computing</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 26-1 to 26-7</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch26">Space-to-space and space-to-Earth communications via quantum entanglement</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch26" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Space-to-space and space-to-Earth communications via quantum entanglement"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Space-to-space and space-to-Earth communications via quantum entanglement</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch26.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Space-to-space and space-to-Earth communications via quantum entanglement" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Space-to-space and space-to-Earth communications via quantum entanglement</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch26.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Space-to-space and space-to-Earth communications via quantum entanglement"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Space-to-space and space-to-Earth communications via quantum entanglement</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 27-1 to 27-8</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch27">Space-to-space quantum interferometric communications</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch27" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Space-to-space quantum interferometric communications"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Space-to-space quantum interferometric communications</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch27.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Space-to-space quantum interferometric communications" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Space-to-space quantum interferometric communications</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch27.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Space-to-space quantum interferometric communications"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Space-to-space quantum interferometric communications</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 28-1 to 28-10</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch28">Quanta pair sources for quantum entanglement experiments</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch28" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quanta pair sources for quantum entanglement experiments"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quanta pair sources for quantum entanglement experiments</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch28.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quanta pair sources for quantum entanglement experiments" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quanta pair sources for quantum entanglement experiments</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch28.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quanta pair sources for quantum entanglement experiments"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quanta pair sources for quantum entanglement experiments</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 29-1 to 29-19</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch29">Quantum interferometric principles</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch29" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="Quantum interferometric principles"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, Quantum interferometric principles</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch29.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Quantum interferometric principles" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Quantum interferometric principles</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch29.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Quantum interferometric principles"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Quantum interferometric principles</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><div class="indexer">Pages 30-1 to 30-17</div><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch30">On the interpretation of quantum mechanics</a></h2><p class="small art-list-item-meta"><span itemtype="http://schema.org/Person" itemprop="author" class="nowrap"><span itemprop="name">F J Duarte</span></span></p><div class="art-list-item-tools small"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch30" class="mr-2 event_book-mini-link" data-event-action="View chapter" title="On the interpretation of quantum mechanics"><span class="icon-article"></span>View chapter<span class="offscreen-hidden">, On the interpretation of quantum mechanics</span></a><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch30.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="On the interpretation of quantum mechanics" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, On the interpretation of quantum mechanics</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch30.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="On the interpretation of quantum mechanics"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, On the interpretation of quantum mechanics</span></a></div></div></div><div class="art-list-item"><div class="art-list-item-body"><h2 class="art-list-item-title"><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch31.pdf">Back matter</a></h2><div class="art-list-item-tools small"><a target="_blank" href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch31.pdf" class="mr-2 event_book-mini-link" data-event-action="PDF" title="Back matter" rel="noopener"><span class="icon-file-pdf"></span>PDF chapter<span class="offscreen-hidden">, Back matter</span></a><a href="/book/mono/978-0-7503-5269-7/chapter/bk978-0-7503-5269-7ch31.epub" class="mr-2 event_book-mini-link" data-event-action="ePub" title="Back matter"><span class="icon-epub"></span><span class="offscreen-hidden">Download </span>ePub chapter<span class="offscreen-hidden">, Back matter</span></a></div></div></div></div></div></div><div tabindex="0" role="tabpanel" id="book-about-tab" aria-labelledby="book-about" hidden=""><div class="tab-content-padding"><div class="article-meta"><div id="wd-bk-pg-extent"><h2 class="replica-h4">Extent</h2><p itemprop="datePublished">334pp</p></div><div id="wd-bk-pg-doi"><h2 class="replica-h4"><abbr title="digital object identifier"><span class="replica-abbr">D O I</span></abbr></h2><p><a itemprop="sameAs" href="https://doi.org/10.1088/978-0-7503-5269-7">https://doi.org/10.1088/978-0-7503-5269-7</a></p></div> <div id="wd-bk-pg-readership"><h2 class="replica-h4">Readership</h2><p>Scientist and engineers working on quantum entanglement programs around the world. An equally relevant market are graduate students. Science professionals and engineering management administering quantum programs.</p></div> <div id="wd-bk-pg-dates"><h2 class="replica-h4">Dates</h2><p itemprop="datePublished">Published September 2022</p></div><div id="wd-bk-pg-bk-links"><h2 class="replica-h4">Books links</h2><p><a href="/page/ePub3">About ePub3</a></p><p><a href="https://ioppublishing.org/publications/our-books/" target="_blank" rel="noopener">About IOP ebooks<svg class="fa-icon fa-icon--right" role="img" focusable="false" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><title>opens in new tab</title><path d="M320 0c-17.7 0-32 14.3-32 32s14.3 32 32 32h82.7L201.4 265.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0L448 109.3V192c0 17.7 14.3 32 32 32s32-14.3 32-32V32c0-17.7-14.3-32-32-32H320zM80 32C35.8 32 0 67.8 0 112V432c0 44.2 35.8 80 80 80H400c44.2 0 80-35.8 80-80V320c0-17.7-14.3-32-32-32s-32 14.3-32 32V432c0 8.8-7.2 16-16 16H80c-8.8 0-16-7.2-16-16V112c0-8.8 7.2-16 16-16H192c17.7 0 32-14.3 32-32s-14.3-32-32-32H80z"/></svg></a></p></div></div></div></div><div tabindex="0" role="tabpanel" id="book-authors-tab" aria-labelledby="book-authors" hidden=""><div class="tab-content-padding"> <div id="wd-bk-pg-about-the-author"><h2 class="replica-h4">About the author</h2><p>F J Duarte is a laser and quantum physicist based in the USA since the 1980s. He has extensive experience in the academic, industrial and defense sectors. He is an editor/author of 15 laser and quantum optics books and sole author of three books (Tunable Laser Optics, Quantum Optics for Engineers, and Fundamentals of Quantum Entanglement). He has made key original contributions to the fields of narrow-linewidth tunable laser oscillators, nanoparticle solid-state laser materials, coherent emission from electrically-pumped organic semiconductors, and laser interferometry. He is also the author of the multiple-prism grating dispersion theory applicable to tunable lasers, laser pulse compression, and coherent microscopy. His contributions have been applied to numerous scientific fields from astronomy to nanophotonics. In 1987 he was elected Fellow of the Australian Institute of Physics, and in 1993 he was elected Fellow of the Optical Society of America. Dr Duarte has been awarded the Engineering Excellence Award and the David Richardson Medal from the Optical Society (Optica).</p></div> </div></div><div tabindex="0" role="tabpanel" id="book-multimedia-tab" aria-labelledby="book-multimedia" hidden=""><div class="tab-content-padding"> <div id="wd-bk-pg-supp-data"><h2 class="replica-h4">Supplementary material</h2><p><a href="https://content.cld.iop.org/books/10__1088_978-0-7503-5269-7/revision7/FQE2ndCorrigenda.pdf?Expires=1740378134&Signature=fS8mX7DZQLcUrsA2R2C-XHZXmwJBA6HEqxUJlX1HZjzdEKz~DyoLEy-psMq08BxKhmJcHHArPAWsx2Pb9eRm0Gu7aEcAEDW23eSXaA2pfAiWiD-UCKbf-EH1Pqf6xiSDexxByhm6JK7mZf7JQuAmqzHlVWeo70eA8WwDlWqO~wTax~DrTvsYyMD8Zqccsre7Yfxb9EpentL2Wf994RIOBeSg~9CV2GCojTZzNQAV9cPAC91b4y3hxbfSiG-DMX1uRPdZBq7tcg4O6OsOEo9AJ5uwLTYrrtGPhwVKjAJwvaz5PH-sEMcmchCQ9OQqLSWMpO2tNxJ12BwOGEp3MIQoEA__&Key-Pair-Id=KL1D8TIY3N7T8" id="bk978-0-7503-5269-7n2">Supplementary material</a> </p></div> </div></div><div tabindex="0" role="tabpanel" id="book-review-tab" aria-labelledby="book-review" hidden=""><div class="tab-content-padding art-list"><br/><div class="art-list-item"><div><p>While good wines and cheeses get better with age, good books require more human intervention. The second edition of Fundamentals of Quantum Entanglement makes an excellent book into an even better one. The second edition has a similar structure to the first, with relatively short and dense but easy-to-follow chapters, most of them packed with advanced math, and all of them including multiple chapter references (many published by the book author). The second edition includes a new chapter on quantum entanglement via matrix notation, as well as many additional sections in the existing chapters. To help the reader digest the sometimes daunting math treatment, the book is illustrated with diagrams and charts (some in color, although not much benefitting from color) and mapped out around a fairly extensive index. While the first edition was already an excellent reference for those interested in quantum entanglement, the second edition could equally well be used as a textbook, because each chapter includes a set of problems.</p><p>Bogdan Hoanca, Optica, October 2023</p></div><div><a href="https://www.optica-opn.org/home/book_reviews/2023/1023/fundamentals_of_quantum_entanglement_second_editio/">https://www.optica-opn.org/home/book_reviews/2023/1023/fundamentals_of_quantum_entanglement_second_editio/</a></div></div></div></div></div></div><div class="da2 ta2"></div></div></main><div class="da3 ta1"><div class="side-and-below"><aside aria-labelledby="book-related-content-heading" class="boxout bdt-6 related" id="wd-related"><h2 id="book-related-content-heading" class="replica-h3">You may also like</h2><div class="related-content-lists"><h3 class="related-article-hd replica-h4">Journal articles</h3><div class="related-article-list"><ul class=""><li><a class="event_book-related-article" href="/article/10.1088/0253-6102/38/5/541">Entanglement Preserving in Quantum Copying of Three-Qubit Entangled State</a></li><li><a class="event_book-related-article" href="/article/10.1088/1402-4896/ac8775">Protecting quantum entanglement in thermal reservoir by detuning</a></li><li><a class="event_book-related-article" href="/article/10.1088/1402-4896/92/2/023004">Quantum entanglement for systems of identical bosons: I. General features</a></li></ul></div><h3 class="related-article-hd replica-h4">Books</h3><div class="related-book-list"><ul class=""><li><a class="event_book-related-book" href="/book/mono/978-0-7503-3963-6">Quantum Computation and Quantum Information Simulation using Python</a></li><li><a class="event_book-related-book" href="/book/edit/978-0-7503-5547-6">Organic Lasers and Organic Photonics (Second Edition)</a></li><li><a class="event_book-related-book" href="/book/mono/978-0-7503-1371-1">Complex Light</a></li></ul></div></div></aside><aside aria-label="Physics World Jobs" class="wd-pw-jobs print-hide"><img height="23" alt="Physics World Jobs" class="pw-jobs-logo mt-025 mb-075" src='data:image/svg+xml;base64,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'><ul><li><div class="cf"><a href="https://www.physicsworldjobs.com/job/20083/?trackid=9&utm_source=RestAPI&utm_medium=Referral&utm_source=IOPscience&utm_medium=organic&utm_campaign=IOPscience&utm_term=2053-2563&utm_content=BOOK">Physics Faculty Positions at Westlake University</a></div><span>Westlake University</span></li><li><div class="cf"><a href="https://www.physicsworldjobs.com/job/19204/?trackid=9&utm_source=RestAPI&utm_medium=Referral&utm_source=IOPscience&utm_medium=organic&utm_campaign=IOPscience&utm_term=2053-2563&utm_content=BOOK">Recruitment of Overseas High-level Talent</a></div><span>Institute of High Energy Physics – Chinese Academy of Sciences</span></li><li><div class="cf"><a href="https://www.physicsworldjobs.com/job/20762/?trackid=9&utm_source=RestAPI&utm_medium=Referral&utm_source=IOPscience&utm_medium=organic&utm_campaign=IOPscience&utm_term=2053-2563&utm_content=BOOK">Postdoc Research Associate - Quantum Materials Synthesis and Characterization, AI-Enabled Automation</a></div><span>Oak Ridge National Laboratory</span></li><li><div class="cf"><a class="fl-l" href="https://www.physicsworldjobs.com/jobs?utm_source=IOPscience&utm_medium=organic&utm_campaign=IOPscience&utm_term=2053-2563&utm_content=BOOK">More jobs</a><a class="right fl-r" href="https://employers.physicsworldjobs.com?utm_source=IOPscience&utm_medium=organic&utm_campaign=IOPscience&utm_term=2053-2563&utm_content=BOOK">Post a job</a></div></li></ul></aside><aside role="complementary" aria-label="Right sidebar adverts"><div id='div-gpt-ad-1669279847892-0' style='min-width: 160px; min-height: 250px;'><script> googletag.cmd.push(function () { googletag.display('div-gpt-ad-1669279847892-0'); }); </script></div></aside></div></div></div></div><div data-scroll-header="" class="data-header-anchor" id="exp"></div><footer class="footer content-grid__full-width" data-footer-content role="contentinfo"><nav aria-label="Further resources" class="footer__grid"><div><h2 class="footer__heading">IOPscience</h2><ul class="footer__list"><li class="footer__item"><a class="link--colour--white" href="/journalList">Journals</a></li><li class="footer__item"><a class="link--colour--white" href="/booklistinfo/home">Books</a></li><li class="footer__item"><a class="link--colour--white" href="/conference-series">IOP Conference Series</a></li><li class="footer__item"><a class="link--colour--white" href="/page/aboutiopscience">About IOPscience</a></li><li class="footer__item"><a class="link--colour--white" href="https://ioppublishing.org/about-us/contact-us/">Contact Us</a></li><li class="footer__item"><a class="link--colour--white" href="/info/page/developing-countries-access">Developing countries access</a></li><li class="footer__item"><a class="link--colour--white" href="https://publishingsupport.iopscience.iop.org/open_access/">IOP Publishing open access policy</a></li><li class="footer__item"><a class="link--colour--white" href="/page/accessibility">Accessibility</a></li></ul></div><div><h2 class="footer__heading">IOP Publishing</h2><ul class="footer__list"><li class="footer__item"><a class="link--colour--white" href="https://ioppublishing.org/legal/copyright/">Copyright 2024 IOP Publishing</a></li><li class="footer__item"><a class="link--colour--white" href="/page/terms">Terms and Conditions</a></li><li class="footer__item"><a class="link--colour--white" href="/page/disclaimer">Disclaimer</a></li><li class="footer__item"><a class="link--colour--white" href="https://ioppublishing.org/legal/privacy-cookies-policy/">Privacy and Cookie Policy</a></li><li class="footer__item"><a class="link--colour--white" href="https://ioppublishing.org/legal/textanddataminingpolicy/">Text and Data mining policy</a></li></ul></div><div><h2 class="footer__heading">Publishing Support</h2><ul class="footer__list"><li class="footer__item"><a class="link--colour--white" href="https://publishingsupport.iopscience.iop.org/" data-ga-event="footer-pub-support-link">Authors</a></li><li class="footer__item"><a class="link--colour--white" href="https://publishingsupport.iopscience.iop.org/publishing-support/reviewers/" data-ga-event="footer-pub-support-link">Reviewers</a></li><li class="footer__item"><a class="link--colour--white" href="https://publishingsupport.iopscience.iop.org/publishing-support/organisers/" data-ga-event="footer-pub-support-link">Conference Organisers</a></li></ul></div></nav><div class="footer__notice"><div class="footer__notice-inner"><div class="footer__notice-text"><svg aria-hidden="true" class="footer__cookie fa-icon" focusable="false" viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg"><path d="M257.5 27.6c-.8-5.4-4.9-9.8-10.3-10.6c-22.1-3.1-44.6 .9-64.4 11.4l-74 39.5C89.1 78.4 73.2 94.9 63.4 115L26.7 190.6c-9.8 20.1-13 42.9-9.1 64.9l14.5 82.8c3.9 22.1 14.6 42.3 30.7 57.9l60.3 58.4c16.1 15.6 36.6 25.6 58.7 28.7l83 11.7c22.1 3.1 44.6-.9 64.4-11.4l74-39.5c19.7-10.5 35.6-27 45.4-47.2l36.7-75.5c9.8-20.1 13-42.9 9.1-64.9c-.9-5.3-5.3-9.3-10.6-10.1c-51.5-8.2-92.8-47.1-104.5-97.4c-1.8-7.6-8-13.4-15.7-14.6c-54.6-8.7-97.7-52-106.2-106.8zM208 144a32 32 0 1 1 0 64 32 32 0 1 1 0-64zM144 336a32 32 0 1 1 64 0 32 32 0 1 1 -64 0zm224-64a32 32 0 1 1 0 64 32 32 0 1 1 0-64z"/></svg><span><strong>This site uses cookies</strong>. By continuing to use this site you agree to our use of cookies.</span></div><div class="footer__socials"><div class="footer__social-icons"><a class="link--colour--white replicate-hover" href="https://twitter.com/ioppublishing?lang=en"><span class="sr-only">IOP Publishing Twitter page</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg"><path d="M459.37 151.716c.325 4.548.325 9.097.325 13.645 0 138.72-105.583 298.558-298.558 298.558-59.452 0-114.68-17.219-161.137-47.106 8.447.974 16.568 1.299 25.34 1.299 49.055 0 94.213-16.568 130.274-44.832-46.132-.975-84.792-31.188-98.112-72.772 6.498.974 12.995 1.624 19.818 1.624 9.421 0 18.843-1.3 27.614-3.573-48.081-9.747-84.143-51.98-84.143-102.985v-1.299c13.969 7.797 30.214 12.67 47.431 13.319-28.264-18.843-46.781-51.005-46.781-87.391 0-19.492 5.197-37.36 14.294-52.954 51.655 63.675 129.3 105.258 216.365 109.807-1.624-7.797-2.599-15.918-2.599-24.04 0-57.828 46.782-104.934 104.934-104.934 30.213 0 57.502 12.67 76.67 33.137 23.715-4.548 46.456-13.32 66.599-25.34-7.798 24.366-24.366 44.833-46.132 57.827 21.117-2.273 41.584-8.122 60.426-16.243-14.292 20.791-32.161 39.308-52.628 54.253z"/></svg></a><a class="link--colour--white replicate-hover" href="https://www.facebook.com/ioppublishing/"><span class="sr-only">IOP Publishing Facebook page</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg"><path d="M504 256C504 119 393 8 256 8S8 119 8 256c0 123.78 90.69 226.38 209.25 245V327.69h-63V256h63v-54.64c0-62.15 37-96.48 93.67-96.48 27.14 0 55.52 4.84 55.52 4.84v61h-31.28c-30.8 0-40.41 19.12-40.41 38.73V256h68.78l-11 71.69h-57.78V501C413.31 482.38 504 379.78 504 256z"/></svg></a><a class="link--colour--white replicate-hover" href="https://www.linkedin.com/company/iop-publishing"><span class="sr-only">IOP Publishing LinkedIn page</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 0 448 512" xmlns="http://www.w3.org/2000/svg"><path d="M100.28 448H7.4V148.9h92.88zM53.79 108.1C24.09 108.1 0 83.5 0 53.8a53.79 53.79 0 0 1 107.58 0c0 29.7-24.1 54.3-53.79 54.3zM447.9 448h-92.68V302.4c0-34.7-.7-79.2-48.29-79.2-48.29 0-55.69 37.7-55.69 76.7V448h-92.78V148.9h89.08v40.8h1.3c12.4-23.5 42.69-48.3 87.88-48.3 94 0 111.28 61.9 111.28 142.3V448z"/></svg></a><a class="link--colour--white replicate-hover" href="https://www.youtube.com/channel/UC6sGrQTcmY8NpmfGEfRqRrg"><span class="sr-only">IOP Publishing Youtube page</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 60 576 395" xmlns="http://www.w3.org/2000/svg"><path d="M549.655 124.083c-6.281-23.65-24.787-42.276-48.284-48.597C458.781 64 288 64 288 64S117.22 64 74.629 75.486c-23.497 6.322-42.003 24.947-48.284 48.597-11.412 42.867-11.412 132.305-11.412 132.305s0 89.438 11.412 132.305c6.281 23.65 24.787 41.5 48.284 47.821C117.22 448 288 448 288 448s170.78 0 213.371-11.486c23.497-6.321 42.003-24.171 48.284-47.821 11.412-42.867 11.412-132.305 11.412-132.305s0-89.438-11.412-132.305zm-317.51 213.508V175.185l142.739 81.205-142.739 81.201z"/></svg></a><a class="link--colour--white replicate-hover" href="https://ioppublishing.org/wp-content/uploads/2020/11/WeChat-QR-Code.png"><span class="sr-only">IOP Publishing WeChat QR code</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 0 576 512" xmlns="http://www.w3.org/2000/svg"><path d="M385.2 167.6c6.4 0 12.6.3 18.8 1.1C387.4 90.3 303.3 32 207.7 32 100.5 32 13 104.8 13 197.4c0 53.4 29.3 97.5 77.9 131.6l-19.3 58.6 68-34.1c24.4 4.8 43.8 9.7 68.2 9.7 6.2 0 12.1-.3 18.3-.8-4-12.9-6.2-26.6-6.2-40.8-.1-84.9 72.9-154 165.3-154zm-104.5-52.9c14.5 0 24.2 9.7 24.2 24.4 0 14.5-9.7 24.2-24.2 24.2-14.8 0-29.3-9.7-29.3-24.2.1-14.7 14.6-24.4 29.3-24.4zm-136.4 48.6c-14.5 0-29.3-9.7-29.3-24.2 0-14.8 14.8-24.4 29.3-24.4 14.8 0 24.4 9.7 24.4 24.4 0 14.6-9.6 24.2-24.4 24.2zM563 319.4c0-77.9-77.9-141.3-165.4-141.3-92.7 0-165.4 63.4-165.4 141.3S305 460.7 397.6 460.7c19.3 0 38.9-5.1 58.6-9.9l53.4 29.3-14.8-48.6C534 402.1 563 363.2 563 319.4zm-219.1-24.5c-9.7 0-19.3-9.7-19.3-19.6 0-9.7 9.7-19.3 19.3-19.3 14.8 0 24.4 9.7 24.4 19.3 0 10-9.7 19.6-24.4 19.6zm107.1 0c-9.7 0-19.3-9.7-19.3-19.6 0-9.7 9.7-19.3 19.3-19.3 14.5 0 24.4 9.7 24.4 19.3.1 10-9.9 19.6-24.4 19.6z"/></svg></a><a class="link--colour--white replicate-hover" href="https://www.weibo.com/u/2931886367"><span class="sr-only">IOP Publishing Weibo page</span><svg aria-hidden="true" class="fa-icon fa-icon--xlrg" focusable="false" viewBox="0 0 512 512" xmlns="http://www.w3.org/2000/svg"><path d="M407 177.6c7.6-24-13.4-46.8-37.4-41.7-22 4.8-28.8-28.1-7.1-32.8 50.1-10.9 92.3 37.1 76.5 84.8-6.8 21.2-38.8 10.8-32-10.3zM214.8 446.7C108.5 446.7 0 395.3 0 310.4c0-44.3 28-95.4 76.3-143.7C176 67 279.5 65.8 249.9 161c-4 13.1 12.3 5.7 12.3 6 79.5-33.6 140.5-16.8 114 51.4-3.7 9.4 1.1 10.9 8.3 13.1 135.7 42.3 34.8 215.2-169.7 215.2zm143.7-146.3c-5.4-55.7-78.5-94-163.4-85.7-84.8 8.6-148.8 60.3-143.4 116s78.5 94 163.4 85.7c84.8-8.6 148.8-60.3 143.4-116zM347.9 35.1c-25.9 5.6-16.8 43.7 8.3 38.3 72.3-15.2 134.8 52.8 111.7 124-7.4 24.2 29.1 37 37.4 12 31.9-99.8-55.1-195.9-157.4-174.3zm-78.5 311c-17.1 38.8-66.8 60-109.1 46.3-40.8-13.1-58-53.4-40.3-89.7 17.7-35.4 63.1-55.4 103.4-45.1 42 10.8 63.1 50.2 46 88.5zm-86.3-30c-12.9-5.4-30 .3-38 12.9-8.3 12.9-4.3 28 8.6 34 13.1 6 30.8.3 39.1-12.9 8-13.1 3.7-28.3-9.7-34zm32.6-13.4c-5.1-1.7-11.4.6-14.3 5.4-2.9 5.1-1.4 10.6 3.7 12.9 5.1 2 11.7-.3 14.6-5.4 2.8-5.2 1.1-10.9-4-12.9z"/></svg></a></div><a href="https://ioppublishing.org/"><img alt="IOP Publishing" class="footer__social-logo" src='data:image/svg+xml;base64,PD94bWwgdmVyc2lvbj0iMS4wIiBlbmNvZGluZz0idXRmLTgiPz4KPCEtLSBHZW5lcmF0b3I6IEFkb2JlIElsbHVzdHJhdG9yIDE4LjEuMCwgU1ZHIEV4cG9ydCBQbHVnLUluIC4gU1ZHIFZlcnNpb246IDYuMDAgQnVpbGQgMCkgIC0tPgo8c3ZnIHZlcnNpb249IjEuMSIgaWQ9IkxheWVyXzEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgeG1sbnM6eGxpbms9Imh0dHA6Ly93d3cudzMub3JnLzE5OTkveGxpbmsiIHg9IjBweCIgeT0iMHB4IgoJIHZpZXdCb3g9IjAgMCAxOTAuNyAyOS44IiBlbmFibGUtYmFja2dyb3VuZD0ibmV3IDAgMCAxOTAuNyAyOS44IiB4bWw6c3BhY2U9InByZXNlcnZlIj4KPHBhdGggZmlsbD0iI2ViMWIyNCIgZD0iTTAsMjMuM1YwLjNoNy4xdjIyLjlIMHoiLz4KPHBhdGggZmlsbD0iI2ViMWIyNCIgZD0iTTIwLjUsMjMuNmMtNi45LDAtMTAuOS01LjItMTAuOS0xMS44YzAtNi43LDQtMTEuOCwxMS0xMS44YzYuOSwwLDEwLjgsNSwxMC44LDExLjYKCUMzMS40LDE4LjIsMjcuNSwyMy42LDIwLjUsMjMuNnogTTIwLjYsNS4yYy0zLjIsMC0zLjUsNC41LTMuNSw2LjhjMCwyLjMsMC4yLDYuNCwzLjQsNi40YzMuMywwLDMuMy00LjIsMy4zLTYuNXYtMC4yCglDMjMuOCw5LjQsMjMuOCw1LjIsMjAuNiw1LjJ6Ii8+CjxwYXRoIGZpbGw9IiNlYjFiMjQiIGQ9Ik00NSwxNWgtNHY4LjNoLTcuMVYwLjNoOS44YzIuNSwwLDUuMiwwLjIsNy4yLDEuOGMxLjcsMS40LDIuNSwzLjMsMi41LDUuNUM1My40LDEyLjUsNDkuNSwxNSw0NSwxNXoKCSBNNDMuNSw1LjZoLTIuNlYxMGgyLjRjMS42LDAsMy4xLTAuMywzLjEtMi4zQzQ2LjMsNiw0NSw1LjYsNDMuNSw1LjZ6Ii8+CjxnPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTcyLjUsMTMuNGMtMiwwLjctNC4zLDAuNS02LjQsMC41djkuM2gtMi44VjAuM2g0LjljMi40LDAsNC44LDAuMiw2LjYsMmMxLjIsMS4zLDEuOCwzLjEsMS44LDQuOAoJCUM3Ni42LDEwLjEsNzUuMywxMi41LDcyLjUsMTMuNHogTTY5LjcsMi42aC0zLjZ2OWgyLjFjMy4zLDAsNS40LTAuNiw1LjQtNC40QzczLjcsNC43LDcyLjQsMi42LDY5LjcsMi42eiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTg4LjUsMjMuM3YtMi41Yy0xLDItMi4xLDMtNC40LDNjLTEuMiwwLTIuNS0wLjMtMy4zLTEuM2MtMS4zLTEuNC0xLjItMy43LTEuMi01LjVWNi4zaDIuNXYxMS4zCgkJYzAsMiwwLDQsMi42LDRjMS44LDAsMi44LTEuMywzLjMtMi45YzAuNS0xLjUsMC40LTMuMSwwLjQtNC43VjYuM2gyLjV2MTYuOUg4OC41eiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTEwMS43LDIzLjZjLTIuMywwLTMuMy0wLjctNC4zLTIuN2MtMC4yLDAuOC0wLjQsMS42LTAuNywyLjRoLTEuM1YwLjNoMi41djguMkM5OSw2LjksMTAwLjIsNiwxMDIuMiw2CgkJYzQuNywwLDUuOSw0LjksNS45LDguN0MxMDguMSwxOSwxMDYuNywyMy42LDEwMS43LDIzLjZ6IE0xMDEuNyw4LjFjLTIuOCwwLTMuOCwzLTMuOCw1LjRWMTZjMCwyLjYsMC42LDUuNSwzLjcsNS41CgkJYzMuNSwwLDMuNy00LjMsMy43LTYuOUMxMDUuMywxMiwxMDUuMiw4LjEsMTAxLjcsOC4xeiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTExMS44LDIzLjNWMC4zaDIuNXYyMi45SDExMS44eiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTExOC43LDMuM3YtM2gyLjh2M0gxMTguN3ogTTExOC44LDIzLjNWNi4zaDIuNXYxNi45SDExOC44eiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTEzMC4yLDIzLjdjLTMuNCwwLTUuNC0xLjUtNi4xLTQuOGwyLjMtMC41YzAuNCwyLjIsMS43LDMuMiwzLjksMy4yYzEuNywwLDMuNC0wLjksMy40LTIuOAoJCWMwLTMuMS01LjQtMi44LTcuNi00LjdjLTAuOS0wLjgtMS40LTItMS40LTMuMmMwLTMuMSwyLjYtNS4xLDUuNS01LjFjMS41LDAsMywwLjUsNC4xLDEuN2MwLjcsMC44LDEsMS42LDEuMywyLjZsLTIuMiwwLjYKCQlDMTMyLjksOS4xLDEzMiw4LDEzMC4yLDhjLTEuNSwwLTIuOSwwLjktMi45LDIuNmMwLDEuNCwxLDIsMi4yLDIuNGMyLjksMC45LDYuOSwxLjcsNi45LDUuNkMxMzYuNCwyMS45LDEzMy40LDIzLjcsMTMwLjIsMjMuN3oiLz4KCTxwYXRoIGZpbGw9IiNGRkZGRkYiIGQ9Ik0xNDguMSwyMy4zVjEyLjdjMC0yLDAuMS00LjgtMi43LTQuOGMtMy4yLDAtMy41LDQuMi0zLjUsNi41djguOGgtMi41VjAuM2gyLjV2OC42YzAuOC0yLDIuMS0zLjEsNC4yLTMuMQoJCWMxLjIsMCwyLjUsMC40LDMuNCwxLjNjMS4zLDEuNCwxLjIsMy43LDEuMiw1LjZ2MTAuNUgxNDguMXoiLz4KCTxwYXRoIGZpbGw9IiNGRkZGRkYiIGQ9Ik0xNTUsMy4zdi0zaDIuOHYzSDE1NXogTTE1NS4xLDIzLjNWNi4zaDIuNXYxNi45SDE1NS4xeiIvPgoJPHBhdGggZmlsbD0iI0ZGRkZGRiIgZD0iTTE3MC45LDIzLjNWMTIuOGMwLTIuMSwwLjItNC44LTIuNi00LjhjLTMuMywwLTMuNiwzLjctMy42LDYuMnY5LjFoLTIuNVY2LjNoMi4zVjkKCQljMC45LTIuMSwyLjEtMy4xLDQuNC0zLjFjMS4zLDAsMi43LDAuNCwzLjUsMS41YzEuMSwxLjQsMSwzLjUsMSw1LjJ2MTAuOEgxNzAuOXoiLz4KCTxwYXRoIGZpbGw9IiNGRkZGRkYiIGQ9Ik0xODMuNSwyOS44Yy0yLjksMC02LjgtMC44LTYuOC00LjVjMC0xLjcsMC43LTIuOCwyLjMtMy40Yy0xLTAuNy0xLjYtMS4zLTEuNi0yLjZjMC0xLjUsMC44LTIuNSwyLjItMy4xCgkJYy0xLjMtMS4zLTEuOS0yLjUtMS45LTQuNWMwLTMuMiwyLjQtNS45LDUuNy01LjljMS4yLDAsMS44LDAuMiwyLjgsMC44YzAuNC0yLjMsMS4zLTIuOSwzLjYtMi45aDAuNHYyLjJjLTAuMiwwLTAuNC0wLjEtMC43LTAuMQoJCWMtMS4zLDAtMS43LDEtMS44LDIuMWMwLjksMS4yLDEuMywyLjMsMS4zLDMuOGMwLDMuMy0yLjQsNS44LTUuNyw1LjhjLTAuNywwLTEuNC0wLjEtMi4xLTAuM2MtMC44LDAuMy0xLjQsMC42LTEuNCwxLjUKCQljMCwxLjUsMS41LDEuNiwyLjYsMS43YzAuNiwwLDEuMiwwLDEuOCwwLjFjMy4yLDAuMiw2LjUsMC4zLDYuNSw0LjNDMTkwLjcsMjguOCwxODYuNywyOS44LDE4My41LDI5Ljh6IE0xODQuMiwyMi42CgkJYy0xLjIsMC0yLjMsMC0zLjUtMC4xYy0wLjksMC41LTEuNCwxLjItMS40LDIuM2MwLDIuNSwyLjMsMi45LDQuNCwyLjljMS45LDAsNC40LTAuNCw0LjQtMi44QzE4OC4xLDIyLjcsMTg1LjgsMjIuNywxODQuMiwyMi42egoJCSBNMTgzLjIsOGMtMi4yLDAtMywxLjktMywzLjhjMCwxLjksMC45LDMuNywzLDMuN2MyLjEsMCwzLjEtMS45LDMuMS0zLjdDMTg2LjQsOS43LDE4NS41LDgsMTgzLjIsOHoiLz4KPC9nPgo8L3N2Zz4K'/></a></div></div></div></footer></div><script> let imgBase = "https://static.iopscience.com/3.80.1/img"; let scriptBase = "https://static.iopscience.com/3.80.1/js"; /* Cutting the mustard - http://responsivenews.co.uk/post/18948466399/cutting-the-mustard */ /* This is the original if statement, from the link above. I have amended it to turn of JS on all IE browsers less than 10. This is due to a function in the iop.jquery.toolbar.js line 35/36. Uses .remove which is not native js supported in IE9 or lower */ /* if('querySelector' in document && 'localStorage' in window && 'addEventListener' in window) { */ /* This is the updated selector, taken from: https://justmarkup.com/log/2015/02/26/cut-the-mustard-revisited/ */ if('visibilityState' in document) { function loadJS( src, cb ){ "use strict"; let ref = window.document.getElementsByTagName( "script" )[ 0 ]; let script = window.document.createElement( "script" ); script.src = src; script.async = true; ref.parentNode.insertBefore( script, ref ); if (cb && typeof(cb) === "function") { script.onload = cb; } return script; } } </script><script>loadJS( scriptBase + "/scripts.min.js" );</script></body></html>