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<span>Conduct of optical Bell test experiments</span> </div> </a> <button aria-controls="toc-Conduct_of_optical_Bell_test_experiments-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Conduct of optical Bell test experiments subsection</span> </button> <ul id="toc-Conduct_of_optical_Bell_test_experiments-sublist" class="vector-toc-list"> <li id="toc-A_typical_CHSH_(two-channel)_experiment" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#A_typical_CHSH_(two-channel)_experiment"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>A typical CHSH (two-channel) experiment</span> </div> </a> <ul id="toc-A_typical_CHSH_(two-channel)_experiment-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-A_typical_CH74_(single-channel)_experiment" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#A_typical_CH74_(single-channel)_experiment"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>A typical CH74 (single-channel) experiment</span> </div> </a> <ul id="toc-A_typical_CH74_(single-channel)_experiment-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Experimental_assumptions" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Experimental_assumptions"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Experimental assumptions</span> </div> </a> <ul id="toc-Experimental_assumptions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notable_experiments" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notable_experiments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notable experiments</span> </div> </a> <button aria-controls="toc-Notable_experiments-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Notable experiments subsection</span> </button> <ul id="toc-Notable_experiments-sublist" class="vector-toc-list"> <li id="toc-Kasday,_Ullman_and_Wu_(1970)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kasday,_Ullman_and_Wu_(1970)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Kasday, Ullman and Wu (1970)</span> </div> </a> <ul id="toc-Kasday,_Ullman_and_Wu_(1970)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Freedman_and_Clauser_(1972)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Freedman_and_Clauser_(1972)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Freedman and Clauser (1972)</span> </div> </a> <ul id="toc-Freedman_and_Clauser_(1972)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Aspect_et_al._(1982)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Aspect_et_al._(1982)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Aspect et al. (1982)</span> </div> </a> <ul id="toc-Aspect_et_al._(1982)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tittel_et_al._(1998)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tittel_et_al._(1998)"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Tittel et al. (1998)</span> </div> </a> <ul id="toc-Tittel_et_al._(1998)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Weihs_et_al._(1998):_experiment_under_"strict_Einstein_locality"_conditions" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Weihs_et_al._(1998):_experiment_under_"strict_Einstein_locality"_conditions"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Weihs et al. (1998): experiment under "strict Einstein locality" conditions</span> </div> </a> <ul id="toc-Weihs_et_al._(1998):_experiment_under_"strict_Einstein_locality"_conditions-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pan_et_al._(2000)_experiment_on_the_GHZ_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Pan_et_al._(2000)_experiment_on_the_GHZ_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Pan et al. (2000) experiment on the GHZ state</span> </div> </a> <ul id="toc-Pan_et_al._(2000)_experiment_on_the_GHZ_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rowe_et_al._(2001):_the_first_to_close_the_detection_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rowe_et_al._(2001):_the_first_to_close_the_detection_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Rowe et al. (2001): the first to close the detection loophole</span> </div> </a> <ul id="toc-Rowe_et_al._(2001):_the_first_to_close_the_detection_loophole-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Go_et_al._(Belle_collaboration):_Observation_of_Bell_inequality_violation_in_B_mesons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Go_et_al._(Belle_collaboration):_Observation_of_Bell_inequality_violation_in_B_mesons"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Go et al. (Belle collaboration): Observation of Bell inequality violation in B mesons</span> </div> </a> <ul id="toc-Go_et_al._(Belle_collaboration):_Observation_of_Bell_inequality_violation_in_B_mesons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Gröblacher_et_al._(2007)_test_of_Leggett-type_non-local_realist_theories" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gröblacher_et_al._(2007)_test_of_Leggett-type_non-local_realist_theories"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.9</span> <span>Gröblacher et al. (2007) test of Leggett-type non-local realist theories</span> </div> </a> <ul id="toc-Gröblacher_et_al._(2007)_test_of_Leggett-type_non-local_realist_theories-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Salart_et_al._(2008):_separation_in_a_Bell_Test" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Salart_et_al._(2008):_separation_in_a_Bell_Test"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.10</span> <span>Salart et al. (2008): separation in a Bell Test</span> </div> </a> <ul id="toc-Salart_et_al._(2008):_separation_in_a_Bell_Test-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ansmann_et_al._(2009):_overcoming_the_detection_loophole_in_solid_state" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ansmann_et_al._(2009):_overcoming_the_detection_loophole_in_solid_state"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.11</span> <span>Ansmann et al. (2009): overcoming the detection loophole in solid state</span> </div> </a> <ul id="toc-Ansmann_et_al._(2009):_overcoming_the_detection_loophole_in_solid_state-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Giustina_et_al._(2013),_Larsson_et_al_(2014):_overcoming_the_detection_loophole_for_photons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Giustina_et_al._(2013),_Larsson_et_al_(2014):_overcoming_the_detection_loophole_for_photons"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.12</span> <span>Giustina et al. (2013), Larsson et al (2014): overcoming the detection loophole for photons</span> </div> </a> <ul id="toc-Giustina_et_al._(2013),_Larsson_et_al_(2014):_overcoming_the_detection_loophole_for_photons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Christensen_et_al._(2013):_overcoming_the_detection_loophole_for_photons" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Christensen_et_al._(2013):_overcoming_the_detection_loophole_for_photons"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.13</span> <span>Christensen et al. (2013): overcoming the detection loophole for photons</span> </div> </a> <ul id="toc-Christensen_et_al._(2013):_overcoming_the_detection_loophole_for_photons-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Hensen_et_al.,_Giustina_et_al.,_Shalm_et_al._(2015):_"loophole-free"_Bell_tests" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Hensen_et_al.,_Giustina_et_al.,_Shalm_et_al._(2015):_"loophole-free"_Bell_tests"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.14</span> <span>Hensen et al., Giustina et al., Shalm et al. (2015): "loophole-free" Bell tests</span> </div> </a> <ul id="toc-Hensen_et_al.,_Giustina_et_al.,_Shalm_et_al._(2015):_"loophole-free"_Bell_tests-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Schmied_et_al._(2016):_Detection_of_Bell_correlations_in_a_many-body_system" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Schmied_et_al._(2016):_Detection_of_Bell_correlations_in_a_many-body_system"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.15</span> <span>Schmied et al. (2016): Detection of Bell correlations in a many-body system</span> </div> </a> <ul id="toc-Schmied_et_al._(2016):_Detection_of_Bell_correlations_in_a_many-body_system-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Handsteiner_et_al._(2017):_"Cosmic_Bell_Test"_-_Measurement_Settings_from_Milky_Way_Stars" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Handsteiner_et_al._(2017):_"Cosmic_Bell_Test"_-_Measurement_Settings_from_Milky_Way_Stars"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.16</span> <span>Handsteiner et al. (2017): "Cosmic Bell Test" - Measurement Settings from Milky Way Stars</span> </div> </a> <ul id="toc-Handsteiner_et_al._(2017):_"Cosmic_Bell_Test"_-_Measurement_Settings_from_Milky_Way_Stars-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rosenfeld_et_al._(2017):_"Event-Ready"_Bell_test_with_entangled_atoms_and_closed_detection_and_locality_loopholes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rosenfeld_et_al._(2017):_"Event-Ready"_Bell_test_with_entangled_atoms_and_closed_detection_and_locality_loopholes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.17</span> <span>Rosenfeld et al. (2017): "Event-Ready" Bell test with entangled atoms and closed detection and locality loopholes</span> </div> </a> <ul id="toc-Rosenfeld_et_al._(2017):_"Event-Ready"_Bell_test_with_entangled_atoms_and_closed_detection_and_locality_loopholes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_BIG_Bell_Test_Collaboration_(2018):_“Challenging_local_realism_with_human_choices”" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#The_BIG_Bell_Test_Collaboration_(2018):_“Challenging_local_realism_with_human_choices”"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.18</span> <span>The BIG Bell Test Collaboration (2018): “Challenging local realism with human choices”</span> </div> </a> <ul id="toc-The_BIG_Bell_Test_Collaboration_(2018):_“Challenging_local_realism_with_human_choices”-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rauch_et_al_(2018):_measurement_settings_from_distant_quasars" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Rauch_et_al_(2018):_measurement_settings_from_distant_quasars"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.19</span> <span>Rauch et al (2018): measurement settings from distant quasars</span> </div> </a> <ul id="toc-Rauch_et_al_(2018):_measurement_settings_from_distant_quasars-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Storz_et_al_(2023):_Loophole-free_Bell_inequality_violation_with_superconducting_circuits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Storz_et_al_(2023):_Loophole-free_Bell_inequality_violation_with_superconducting_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.20</span> <span>Storz et al (2023): Loophole-free Bell inequality violation with superconducting circuits</span> </div> </a> <ul id="toc-Storz_et_al_(2023):_Loophole-free_Bell_inequality_violation_with_superconducting_circuits-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Loopholes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Loopholes"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Loopholes</span> </div> </a> <button aria-controls="toc-Loopholes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Loopholes subsection</span> </button> <ul id="toc-Loopholes-sublist" class="vector-toc-list"> <li id="toc-Detection_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Detection_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Detection loophole</span> </div> </a> <ul id="toc-Detection_loophole-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Locality_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Locality_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Locality loophole</span> </div> </a> <ul id="toc-Locality_loophole-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Coincidence_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Coincidence_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Coincidence loophole</span> </div> </a> <ul id="toc-Coincidence_loophole-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Memory_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Memory_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Memory loophole</span> </div> </a> <ul id="toc-Memory_loophole-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Superdeterminism" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Superdeterminism"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.5</span> <span>Superdeterminism</span> </div> </a> <ul id="toc-Superdeterminism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Many-worlds_loophole" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Many-worlds_loophole"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.6</span> <span>Many-worlds loophole</span> </div> </a> <ul id="toc-Many-worlds_loophole-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Experiments to test Bell's theorem in quantum mechanics</div><style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Bell experiment" redirects here. 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rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist nowraplinks" style="width:19.0em;"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></th></tr><tr><td class="sidebar-image"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi mathvariant="normal">Ψ</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1799e4a910c7d26396922a20ef5ceec25ca1871c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.882ex; height:5.509ex;" alt="{\displaystyle i\hbar {\frac {d}{dt}}|\Psi \rangle ={\hat {H}}|\Psi \rangle }"></span><div class="sidebar-caption" style="font-size:90%;padding-top:0.4em;font-style:italic;"><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger equation</a></div></td></tr><tr><td class="sidebar-above hlist nowrap" style="display:block;margin-bottom:0.4em;"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a></li></ul></td></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Background</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Fundamentals</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)">Complementarity</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_number" title="Quantum number">Quantum number</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">State</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li></ul></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Experiments</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a class="mw-selflink selflink">Bell's inequality</a></li> <li><a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Leggett_inequality" title="Leggett inequality">Leggett inequality</a></li> <li><a href="/wiki/Leggett%E2%80%93Garg_inequality" title="Leggett–Garg inequality">Leggett–Garg inequality</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li></ul> </div> <ul><li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a> <ul><li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice</a></li></ul></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed-choice</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Formulations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Overview</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase-space</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Sum-over-histories (path integral)</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Equations</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective-collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Advanced topics</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a></li> <li><a href="/wiki/Quantum_information_science" title="Quantum information science">Quantum information science</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;border-bottom:1px solid #aaa;"><div class="hlist"> <ul><li><a href="/wiki/Yakir_Aharonov" title="Yakir Aharonov">Aharonov</a></li> <li><a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">Bell</a></li> <li><a href="/wiki/Hans_Bethe" title="Hans Bethe">Bethe</a></li> <li><a href="/wiki/Patrick_Blackett" title="Patrick Blackett">Blackett</a></li> <li><a href="/wiki/Felix_Bloch" title="Felix Bloch">Bloch</a></li> <li><a href="/wiki/David_Bohm" title="David Bohm">Bohm</a></li> <li><a href="/wiki/Niels_Bohr" title="Niels Bohr">Bohr</a></li> <li><a href="/wiki/Max_Born" title="Max Born">Born</a></li> <li><a href="/wiki/Satyendra_Nath_Bose" title="Satyendra Nath Bose">Bose</a></li> <li><a href="/wiki/Louis_de_Broglie" title="Louis de Broglie">de Broglie</a></li> <li><a href="/wiki/Arthur_Compton" title="Arthur Compton">Compton</a></li> <li><a href="/wiki/Paul_Dirac" title="Paul Dirac">Dirac</a></li> <li><a href="/wiki/Clinton_Davisson" title="Clinton Davisson">Davisson</a></li> <li><a href="/wiki/Peter_Debye" title="Peter Debye">Debye</a></li> <li><a href="/wiki/Paul_Ehrenfest" title="Paul Ehrenfest">Ehrenfest</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Everett</a></li> <li><a href="/wiki/Vladimir_Fock" title="Vladimir Fock">Fock</a></li> <li><a href="/wiki/Enrico_Fermi" title="Enrico Fermi">Fermi</a></li> <li><a href="/wiki/Richard_Feynman" title="Richard Feynman">Feynman</a></li> <li><a href="/wiki/Roy_J._Glauber" title="Roy J. Glauber">Glauber</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Gutzwiller</a></li> <li><a href="/wiki/Werner_Heisenberg" title="Werner Heisenberg">Heisenberg</a></li> <li><a href="/wiki/David_Hilbert" title="David Hilbert">Hilbert</a></li> <li><a href="/wiki/Pascual_Jordan" title="Pascual Jordan">Jordan</a></li> <li><a href="/wiki/Hans_Kramers" title="Hans Kramers">Kramers</a></li> <li><a href="/wiki/Willis_Lamb" title="Willis Lamb">Lamb</a></li> <li><a href="/wiki/Lev_Landau" title="Lev Landau">Landau</a></li> <li><a href="/wiki/Max_von_Laue" title="Max von Laue">Laue</a></li> <li><a href="/wiki/Henry_Moseley" title="Henry Moseley">Moseley</a></li> <li><a href="/wiki/Robert_Andrews_Millikan" title="Robert Andrews Millikan">Millikan</a></li> <li><a href="/wiki/Heike_Kamerlingh_Onnes" title="Heike Kamerlingh Onnes">Onnes</a></li> <li><a href="/wiki/Wolfgang_Pauli" title="Wolfgang Pauli">Pauli</a></li> <li><a href="/wiki/Max_Planck" title="Max Planck">Planck</a></li> <li><a href="/wiki/Isidor_Isaac_Rabi" title="Isidor Isaac Rabi">Rabi</a></li> <li><a href="/wiki/C._V._Raman" title="C. V. Raman">Raman</a></li> <li><a href="/wiki/Johannes_Rydberg" title="Johannes Rydberg">Rydberg</a></li> <li><a href="/wiki/Erwin_Schr%C3%B6dinger" title="Erwin Schrödinger">Schrödinger</a></li> <li><a href="/wiki/Michelle_Simmons" title="Michelle Simmons">Simmons</a></li> <li><a href="/wiki/Arnold_Sommerfeld" title="Arnold Sommerfeld">Sommerfeld</a></li> <li><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann</a></li> <li><a href="/wiki/Hermann_Weyl" title="Hermann Weyl">Weyl</a></li> <li><a href="/wiki/Wilhelm_Wien" title="Wilhelm Wien">Wien</a></li> <li><a href="/wiki/Eugene_Wigner" title="Eugene Wigner">Wigner</a></li> <li><a href="/wiki/Pieter_Zeeman" title="Pieter Zeeman">Zeeman</a></li> <li><a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Zeilinger</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar" style="border-top:1px solid #aaa;padding-top:0.1em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_mechanics" title="Template:Quantum mechanics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics" title="Template talk:Quantum mechanics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics" title="Special:EditPage/Template:Quantum mechanics"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>A <b>Bell test</b>, also known as <b>Bell inequality test</b> or <b>Bell experiment</b>, is a real-world <a href="/wiki/Physics" title="Physics">physics</a> experiment designed to test the theory of <a href="/wiki/Quantum_mechanics" title="Quantum mechanics">quantum mechanics</a> in relation to <a href="/wiki/Albert_Einstein" title="Albert Einstein">Albert Einstein</a>'s concept of <a href="/wiki/Local_realism" class="mw-redirect" title="Local realism">local realism</a>. Named for <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Stewart Bell</a>, the experiments test whether or not the real world satisfies local realism, which requires the presence of some <a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">additional local variables</a> (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like <a href="/wiki/Photon" title="Photon">photons</a> and <a href="/wiki/Electron" title="Electron">electrons</a>. The test empirically evaluates the implications of <a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's theorem</a>. As of 2015<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Bell_test&action=edit">[update]</a></sup>, all Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems behave.<sup id="cite_ref-Markoff_1-0" class="reference"><a href="#cite_note-Markoff-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Many types of Bell tests have been performed in physics laboratories, often with the goal of ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of <a href="/wiki/Aspect%27s_experiment" title="Aspect's experiment">earlier Bell tests</a>. This is known as "closing <a href="/wiki/Loopholes_in_Bell_tests" class="mw-redirect" title="Loopholes in Bell tests">loopholes in Bell tests</a>".<sup id="cite_ref-Markoff_1-1" class="reference"><a href="#cite_note-Markoff-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Bell inequality violations are also used in some <a href="/wiki/Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a> <a href="/wiki/Cryptographic_protocol" title="Cryptographic protocol">protocols</a>, whereby a spy's presence is detected when Bell's inequalities <i>cease</i> to be violated. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Bell%27s_theorem" title="Bell's theorem">Bell's theorem</a></div> <p>The Bell test has its origins in the debate between Einstein and other pioneers of quantum physics, principally <a href="/wiki/Niels_Bohr" title="Niels Bohr">Niels Bohr</a>. One feature of the theory of quantum mechanics under debate was the meaning of <a href="/wiki/Heisenberg%27s_uncertainty_principle" class="mw-redirect" title="Heisenberg's uncertainty principle">Heisenberg's uncertainty principle</a>. This principle states that if some information is known about a given particle, there is some other information about it that is impossible to know. An example of this is found in observations of the position and the momentum of a given particle. According to the uncertainty principle, a particle's momentum and its position cannot simultaneously be determined with arbitrarily high precision.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>In 1935, Einstein, <a href="/wiki/Boris_Podolsky" title="Boris Podolsky">Boris Podolsky</a>, and <a href="/wiki/Nathan_Rosen" title="Nathan Rosen">Nathan Rosen</a> published a claim that quantum mechanics predicts that more information about a pair of <a href="/wiki/Quantum_entanglement" title="Quantum entanglement">entangled particles</a> could be observed than Heisenberg's principle allowed, which would only be possible if information were travelling instantly between the two particles. This produces a <a href="/wiki/Paradox" title="Paradox">paradox</a> which came to be known as the "<a href="/wiki/EPR_paradox" class="mw-redirect" title="EPR paradox">EPR paradox</a>" after the three authors. It arises if any effect felt in one location is not the result of a cause that occurred in its <a href="/wiki/Light_cone" title="Light cone">past light cone</a>, relative to its location. This <a href="/wiki/Action_at_a_distance" title="Action at a distance">action at a distance</a> seems to violate <a href="/wiki/Causality_(physics)" title="Causality (physics)">causality</a>, by allowing information between the two locations to travel faster than the speed of light.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> However, it is a common misconception to think that any information can be shared between two observers faster than the speed of light using entangled particles; the hypothetical information transfer here is between the particles. See <a href="/wiki/No-communication_theorem" title="No-communication theorem">no-communication theorem</a> for further explanation. </p><p>Based on this, the authors concluded that the quantum wave function does not provide a complete description of reality. They suggested that there must be some local hidden variables at work in order to account for the behavior of entangled particles. In a theory of hidden variables, as Einstein envisaged it, the randomness and indeterminacy seen in the behavior of quantum particles would only be apparent. For example, if one knew the details of all the hidden variables associated with a particle, then one could predict both its position and momentum. The uncertainty that had been quantified by Heisenberg's principle would simply be an artifact of not having complete information about the hidden variables. Furthermore, Einstein argued that the hidden variables should obey the condition of locality: Whatever the hidden variables actually are, the behavior of the hidden variables for one particle should not be able to instantly affect the behavior of those for another particle far away. This idea, called the <a href="/wiki/Principle_of_locality" title="Principle of locality">principle of locality</a>, is rooted in intuition from classical physics that physical interactions do not propagate instantly across space. These ideas were the subject of ongoing debate between their proponents. In particular, Einstein himself did not approve of the way Podolsky had stated the problem in the famous EPR paper.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In 1964, <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Stewart Bell</a> proposed his famous theorem, which states that no physical theory of hidden local variables can ever reproduce all the predictions of quantum mechanics. Implicit in the theorem is the proposition that the determinism of classical physics is fundamentally incapable of describing quantum mechanics. Bell expanded on the theorem to provide what would become the conceptual foundation of the Bell test experiments.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> </p><p>A typical experiment involves the observation of particles, often photons, in an apparatus designed to produce entangled pairs and allow for the measurement of some characteristic of each, such as their <a href="/wiki/Spin_(physics)" title="Spin (physics)">spin</a>. The results of the experiment could then be compared to what was predicted by local realism and those predicted by quantum mechanics.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> </p><p>In theory, the results could be "coincidentally" consistent with both. To address this problem, Bell proposed a mathematical description of local realism that placed a statistical limit on the likelihood of that eventuality. If the results of an experiment violate Bell's inequality, local hidden variables can be ruled out as their cause. Later researchers built on Bell's work by proposing new inequalities that serve the same purpose and refine the basic idea in one way or another.<sup id="cite_ref-Clauser-1969_5-0" class="reference"><a href="#cite_note-Clauser-1969-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Consequently, the term "Bell inequality" can mean any one of a number of inequalities satisfied by local hidden-variables theories; in practice, many present-day experiments employ the <a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a>. All these inequalities, like the original devised by Bell, express the idea that assuming local realism places restrictions on the statistical results of experiments on sets of particles that have taken part in an interaction and then separated.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> </p><p>To date, all Bell tests have supported the theory of quantum physics, and not the hypothesis of local hidden variables. These efforts to experimentally validate violations of the Bell inequalities resulted in <a href="/wiki/John_Clauser" title="John Clauser">John Clauser</a>, <a href="/wiki/Alain_Aspect" title="Alain Aspect">Alain Aspect</a>, and <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Anton Zeilinger</a> being awarded the 2022 <a href="/wiki/Nobel_Prize_in_Physics" title="Nobel Prize in Physics">Nobel Prize in Physics</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Conduct_of_optical_Bell_test_experiments">Conduct of optical Bell test experiments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=2" title="Edit section: Conduct of optical Bell test experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In practice most actual experiments have used light, assumed to be emitted in the form of particle-like photons (produced by <a href="/wiki/Atomic_cascade" class="mw-redirect" title="Atomic cascade">atomic cascade</a> or <a href="/wiki/Spontaneous_parametric_down_conversion" class="mw-redirect" title="Spontaneous parametric down conversion">spontaneous parametric down conversion</a>), rather than the atoms that Bell originally had in mind. The property of interest is, in the best known experiments, the <a href="/wiki/Polarisation_(waves)" class="mw-redirect" title="Polarisation (waves)">polarisation</a> direction, though other properties can be used. Such experiments fall into two classes, depending on whether the analysers used have one or two output channels. </p> <div class="mw-heading mw-heading3"><h3 id="A_typical_CHSH_(two-channel)_experiment"><span id="A_typical_CHSH_.28two-channel.29_experiment"></span>A typical CHSH (two-channel) experiment</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=3" title="Edit section: A typical CHSH (two-channel) experiment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Two_channel_bell_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Two_channel_bell_test.svg/300px-Two_channel_bell_test.svg.png" decoding="async" width="300" height="107" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/Two_channel_bell_test.svg/450px-Two_channel_bell_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/Two_channel_bell_test.svg/600px-Two_channel_bell_test.svg.png 2x" data-file-width="670" data-file-height="240" /></a><figcaption><b>Scheme of a "two-channel" Bell test</b><br />The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a two-channel polariser whose orientation can be set by the experimenter. Emerging signals from each channel are detected and coincidences counted by the coincidence monitor CM.</figcaption></figure> <p>The diagram shows a typical optical experiment of the two-channel kind for which <a href="/wiki/Alain_Aspect" title="Alain Aspect">Alain Aspect</a> set a precedent in 1982.<sup id="cite_ref-Aspect-1982a_8-0" class="reference"><a href="#cite_note-Aspect-1982a-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Coincidences (simultaneous detections) are recorded, the results being categorised as '++', '+−', '−+' or '−−' and corresponding counts accumulated. </p><p>Four separate subexperiments are conducted, corresponding to the four terms <i>E</i>(<i>a</i>, <i>b</i>) in the test statistic <i>S</i> (equation (2) shown below). The settings <i>a</i>, <i>a</i>′, <i>b</i> and <i>b</i>′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality. </p><p>For each selected value of <i>a</i> and <i>b</i>, the numbers of coincidences in each category (<i>N</i><sub>++</sub>, <i>N</i><sub>−−</sub>, <i>N</i><sub>+−</sub> and <i>N</i><sub>−+</sub>) are recorded. The experimental estimate for <i>E</i>(<i>a</i>, <i>b</i>) is then calculated as: </p> <style data-mw-deduplicate="TemplateStyles:r1266403038">.mw-parser-output table.numblk{border-collapse:collapse;border:none;margin-top:0;margin-right:0;margin-bottom:0}.mw-parser-output table.numblk>tbody>tr>td{vertical-align:middle;padding:0}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2){width:99%}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table{border-collapse:collapse;margin:0;border:none;width:100%}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:first-child,.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:last-child{padding:0 0.4ex}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td:nth-child(2){width:100%;padding:0}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{padding:0}.mw-parser-output table.numblk>tbody>tr>td:last-child{font-weight:bold}.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child{font-weight:unset}.mw-parser-output table.numblk>tbody>tr>td:last-child::before{content:"("}.mw-parser-output table.numblk>tbody>tr>td:last-child::after{content:")"}.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child::before,.mw-parser-output table.numblk.numblk-raw-n>tbody>tr>td:last-child::after{content:none}.mw-parser-output table.numblk>tbody>tr>td{border:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td{border:thin solid}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td{border:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td:nth-child(2)>table>tbody>tr:first-child>td{border:thin solid}.mw-parser-output table.numblk>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{border-left:none;border-right:none;border-bottom:none}.mw-parser-output table.numblk.numblk-border>tbody>tr>td:nth-child(2)>table>tbody>tr:last-child>td{border-left:thin solid;border-right:thin solid;border-bottom:thin solid}.mw-parser-output table.numblk:target{color:var(--color-base,#202122);background-color:#cfe8fd}@media screen{html.skin-theme-clientpref-night .mw-parser-output table.numblk:target{color:var(--color-base,#eaecf0);background-color:#301702}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output table.numblk:target{color:var(--color-base,#eaecf0);background-color:#301702}}</style><table role="presentation" class="numblk" style="margin-left: 1.6em;"><tbody><tr><td class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E={\frac {N_{++}-N_{+-}-N_{-+}+N_{--}}{N_{++}+N_{+-}+N_{-+}+N_{--}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mo>+</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mo>−</mo> </mrow> </msub> <mo>−</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo>+</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo>−</mo> </mrow> </msub> </mrow> <mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mo>+</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> <mo>−</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo>+</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo>−</mo> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E={\frac {N_{++}-N_{+-}-N_{-+}+N_{--}}{N_{++}+N_{+-}+N_{-+}+N_{--}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5b1eff31228c7f31a0d6a0e5718a5d156d10f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.854ex; height:5.843ex;" alt="{\displaystyle E={\frac {N_{++}-N_{+-}-N_{-+}+N_{--}}{N_{++}+N_{+-}+N_{-+}+N_{--}}}}"></span></td> <td></td> <td class="nowrap"><span id="math_1" class="reference nourlexpansion" style="font-weight:bold;">1</span></td></tr></tbody></table> <p>Once all four <i>E</i>’s have been estimated, an experimental estimate of the test statistic </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1266403038"><table role="presentation" class="numblk" style="margin-left: 1.6em;"><tbody><tr><td class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S=E(a,b)-E\left(a,b'\right)+E\left(a',b\right)+E\left(a',b'\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mi>E</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>E</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>,</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>E</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>a</mi> <mo>′</mo> </msup> <mo>,</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mi>E</mi> <mrow> <mo>(</mo> <mrow> <msup> <mi>a</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S=E(a,b)-E\left(a,b'\right)+E\left(a',b\right)+E\left(a',b'\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f70928054f685c09ca5f8bf4eeefda0d71b5f86a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:45.438ex; height:3.009ex;" alt="{\displaystyle S=E(a,b)-E\left(a,b'\right)+E\left(a',b\right)+E\left(a',b'\right).}"></span></td> <td></td> <td class="nowrap"><span id="math_2" class="reference nourlexpansion" style="font-weight:bold;">2</span></td></tr></tbody></table> <p>can be found. If <i>S</i> is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden-variable theories. </p><p>A strong assumption has had to be made, however, to justify use of expression (2), namely, that the sample of detected pairs is representative of the pairs emitted by the source. Denial of this assumption is called the <a href="/wiki/Loopholes_in_Bell_test_experiments" class="mw-redirect" title="Loopholes in Bell test experiments">fair sampling loophole</a>. </p> <div class="mw-heading mw-heading3"><h3 id="A_typical_CH74_(single-channel)_experiment"><span id="A_typical_CH74_.28single-channel.29_experiment"></span>A typical CH74 (single-channel) experiment</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=4" title="Edit section: A typical CH74 (single-channel) experiment"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Single-channel_Bell_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Single-channel_Bell_test.svg/300px-Single-channel_Bell_test.svg.png" decoding="async" width="300" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Single-channel_Bell_test.svg/450px-Single-channel_Bell_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Single-channel_Bell_test.svg/600px-Single-channel_Bell_test.svg.png 2x" data-file-width="723" data-file-height="229" /></a><figcaption><b>Setup for a "single-channel" Bell test</b><br />The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a single channel (e.g. "pile of plates") polariser whose orientation can be set by the experimenter. Emerging signals are detected and coincidences counted by the coincidence monitor CM.</figcaption></figure> <p>Prior to 1982 all actual Bell tests used "single-channel" polarisers and variations on an inequality designed for this setup. The latter is described in Clauser, Horne, Shimony and Holt's much-cited 1969 article as being the one suitable for practical use.<sup id="cite_ref-Clauser-1969_5-1" class="reference"><a href="#cite_note-Clauser-1969-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> As with the CHSH test, there are four subexperiments in which each polariser takes one of two possible settings, but in addition there are other subexperiments in which one or other polariser or both are absent. Counts are taken as before and used to estimate the test statistic. </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1266403038"><table role="presentation" class="numblk" style="margin-left: 1.6em;"><tbody><tr><td class="nowrap"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S={\frac {N(a,b)-N(a,b')+N(a',b)+N(a',b')-N(a',\infty )-N(\infty ,b)}{N(\infty ,\infty )}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mi>N</mi> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mo>′</mo> </msup> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>N</mi> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mo>′</mo> </msup> <mo>,</mo> <msup> <mi>b</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <mi>N</mi> <mo stretchy="false">(</mo> <msup> <mi>a</mi> <mo>′</mo> </msup> <mo>,</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∞</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>N</mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∞</mi> <mo>,</mo> <mi mathvariant="normal">∞</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S={\frac {N(a,b)-N(a,b')+N(a',b)+N(a',b')-N(a',\infty )-N(\infty ,b)}{N(\infty ,\infty )}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b548e1f1317de6d6ea2f5dd0656fa72005bb435" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:68.932ex; height:6.509ex;" alt="{\displaystyle S={\frac {N(a,b)-N(a,b')+N(a',b)+N(a',b')-N(a',\infty )-N(\infty ,b)}{N(\infty ,\infty )}},}"></span></td> <td></td> <td class="nowrap"><span id="math_3" class="reference nourlexpansion" style="font-weight:bold;">3</span></td></tr></tbody></table> <p>where the symbol ∞ indicates absence of a polariser. </p><p>If <i>S</i> exceeds 0 then the experiment is declared to have infringed the CH inequality and hence to have refuted local hidden-variables. This inequality is known as CH inequality instead of CHSH as it was also derived in a 1974 article by Clauser and Horne more rigorously and under weaker assumptions.<sup id="cite_ref-Clauser-1974_9-0" class="reference"><a href="#cite_note-Clauser-1974-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Experimental_assumptions">Experimental assumptions</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=5" title="Edit section: Experimental assumptions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In addition to the theoretical assumptions, there are practical ones. There may, for example, be a number of "accidental coincidences" in addition to those of interest. It is assumed that no bias is introduced by subtracting their estimated number before calculating <i>S</i>, but that this is true is not considered by some to be obvious. There may be synchronisation problems — ambiguity in recognising pairs because in practice they will not be detected at <i>exactly</i> the same time. </p><p>Nevertheless, despite all the deficiencies of the actual experiments, one striking fact emerges: the results are, to a very good approximation, what quantum mechanics predicts. If imperfect experiments give us such excellent overlap with quantum predictions, most working quantum physicists would agree with <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Bell</a> in expecting that, when a perfect Bell test is done, the Bell inequalities will still be violated. This attitude has led to the emergence of a new sub-field of physics known as <a href="/wiki/Quantum_information_theory" class="mw-redirect" title="Quantum information theory">quantum information theory</a>. One of the main achievements of this new branch of physics is showing that violation of Bell's inequalities leads to the possibility of a secure information transfer, which utilizes the so-called <a href="/wiki/Quantum_cryptography" title="Quantum cryptography">quantum cryptography</a> (involving entangled states of pairs of particles). </p> <div class="mw-heading mw-heading2"><h2 id="Notable_experiments">Notable experiments</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=6" title="Edit section: Notable experiments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Over the past half century, a great number of Bell test experiments have been conducted. The experiments are commonly interpreted to rule out local hidden-variable theories, and in 2015 an experiment was performed that is not subject to either the locality loophole or the detection loophole (Hensen et al.<sup id="cite_ref-Hensen_et_al._10-0" class="reference"><a href="#cite_note-Hensen_et_al.-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>). An experiment free of the locality loophole is one where for each separate measurement and in each wing of the experiment, a new setting is chosen and the measurement completed before signals could communicate the settings from one wing of the experiment to the other. An experiment free of the detection loophole is one where close to 100% of the successful measurement outcomes in one wing of the experiment are paired with a successful measurement in the other wing. This percentage is called the efficiency of the experiment. Advancements in technology have led to a great variety of methods to test Bell-type inequalities. </p><p>Some of the best known and recent experiments include: </p> <div class="mw-heading mw-heading3"><h3 id="Kasday,_Ullman_and_Wu_(1970)"><span id="Kasday.2C_Ullman_and_Wu_.281970.29"></span>Kasday, Ullman and Wu (1970)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=7" title="Edit section: Kasday, Ullman and Wu (1970)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Leonard_Ralph_Kasday&action=edit&redlink=1" class="new" title="Leonard Ralph Kasday (page does not exist)">Leonard Ralph Kasday</a>, <a href="/w/index.php?title=Jack_R._Ullman&action=edit&redlink=1" class="new" title="Jack R. Ullman (page does not exist)">Jack R. Ullman</a> and <a href="/wiki/Chien-Shiung_Wu" title="Chien-Shiung Wu">Chien-Shiung Wu</a> carried out the first experimental Bell test, using photon pairs produced by <a href="/wiki/Positronium" title="Positronium">positronium</a> decay and analyzed by <a href="/wiki/Compton_scattering" title="Compton scattering">Compton scattering</a>. The experiment observed photon polarization correlations consistent with quantum predictions and inconsistent with local realistic models that obey the known polarization dependence of Compton scattering. Due to the low polarization selectivity of Compton scattering, the results did not violate a Bell inequality.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Freedman_and_Clauser_(1972)"><span id="Freedman_and_Clauser_.281972.29"></span>Freedman and Clauser (1972)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=8" title="Edit section: Freedman and Clauser (1972)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Stuart_J._Freedman" class="mw-redirect" title="Stuart J. Freedman">Stuart J. Freedman</a> and <a href="/wiki/John_Clauser" title="John Clauser">John Clauser</a> carried out the first Bell test that observed a Bell inequality violation, using Freedman's inequality, a variant on the <a href="/wiki/Clauser_and_Horne%27s_1974_Bell_test" class="mw-redirect" title="Clauser and Horne's 1974 Bell test">CH74 inequality</a>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Aspect_et_al._(1982)"><span id="Aspect_et_al._.281982.29"></span>Aspect et al. (1982)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=9" title="Edit section: Aspect et al. (1982)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Aspect%27s_experiment" title="Aspect's experiment">Aspect's experiment</a></div> <p><a href="/wiki/Alain_Aspect" title="Alain Aspect">Alain Aspect</a> and his team at Orsay, Paris, conducted three Bell tests using calcium cascade sources. The first and last used the <a href="/wiki/Clauser_and_Horne%27s_1974_Bell_test" class="mw-redirect" title="Clauser and Horne's 1974 Bell test">CH74 inequality</a>. The second was the first application of the <a href="/wiki/CHSH_Bell_test" class="mw-redirect" title="CHSH Bell test">CHSH inequality</a>. The third (and most famous) was arranged such that the choice between the two settings on each side was made during the flight of the photons (as originally suggested by <a href="/wiki/John_Stewart_Bell" title="John Stewart Bell">John Bell</a>).<sup id="cite_ref-Aspect-1981_14-0" class="reference"><a href="#cite_note-Aspect-1981-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Aspect-1982b_15-0" class="reference"><a href="#cite_note-Aspect-1982b-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Tittel_et_al._(1998)"><span id="Tittel_et_al._.281998.29"></span>Tittel et al. (1998)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=10" title="Edit section: Tittel et al. (1998)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Geneva 1998 Bell test experiments showed that distance did not destroy the "entanglement". Light was sent in fibre optic cables over distances of several kilometers before it was analysed. As with almost all Bell tests since about 1985, a "parametric down-conversion" (PDC) source was used.<sup id="cite_ref-Title-1998a_16-0" class="reference"><a href="#cite_note-Title-1998a-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Title-1998b_17-0" class="reference"><a href="#cite_note-Title-1998b-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Weihs_et_al._(1998):_experiment_under_"strict_Einstein_locality"_conditions"><span id="Weihs_et_al._.281998.29:_experiment_under_.22strict_Einstein_locality.22_conditions"></span>Weihs et al. (1998): experiment under "strict Einstein locality" conditions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=11" title="Edit section: Weihs et al. (1998): experiment under "strict Einstein locality" conditions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1998 Gregor Weihs and a team at Innsbruck, led by <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Anton Zeilinger</a>, conducted an experiment that closed the "locality" loophole, improving on Aspect's of 1982. The choice of detector was made using a quantum process to ensure that it was random. This test violated the <a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a> by over 30 standard deviations, the coincidence curves agreeing with those predicted by quantum theory.<sup id="cite_ref-Weihs-1998_18-0" class="reference"><a href="#cite_note-Weihs-1998-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Pan_et_al._(2000)_experiment_on_the_GHZ_state"><span id="Pan_et_al._.282000.29_experiment_on_the_GHZ_state"></span>Pan et al. (2000) experiment on the GHZ state</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=12" title="Edit section: Pan et al. (2000) experiment on the GHZ state"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This is the first of new Bell-type experiments on more than two particles; this one uses the so-called <a href="/wiki/Greenberger-Horne-Zeilinger_state" class="mw-redirect" title="Greenberger-Horne-Zeilinger state">GHZ state</a> of three particles.<sup id="cite_ref-GHZ2000_19-0" class="reference"><a href="#cite_note-GHZ2000-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Rowe_et_al._(2001):_the_first_to_close_the_detection_loophole"><span id="Rowe_et_al._.282001.29:_the_first_to_close_the_detection_loophole"></span>Rowe et al. (2001): the first to close the detection loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=13" title="Edit section: Rowe et al. (2001): the first to close the detection loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The detection loophole was first closed in an experiment with two entangled trapped ions, carried out in the ion storage group of David Wineland at the National Institute of Standards and Technology in Boulder. The experiment had detection efficiencies well over 90%.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Go_et_al._(Belle_collaboration):_Observation_of_Bell_inequality_violation_in_B_mesons"><span id="Go_et_al._.28Belle_collaboration.29:_Observation_of_Bell_inequality_violation_in_B_mesons"></span>Go et al. (Belle collaboration): Observation of Bell inequality violation in B mesons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=14" title="Edit section: Go et al. (Belle collaboration): Observation of Bell inequality violation in B mesons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Using semileptonic B0 decays of Υ(4S) at Belle experiment, a clear violation of Bell Inequality in particle-antiparticle correlation is observed.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Gröblacher_et_al._(2007)_test_of_Leggett-type_non-local_realist_theories"><span id="Gr.C3.B6blacher_et_al._.282007.29_test_of_Leggett-type_non-local_realist_theories"></span>Gröblacher et al. (2007) test of Leggett-type non-local realist theories</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=15" title="Edit section: Gröblacher et al. (2007) test of Leggett-type non-local realist theories"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A specific class of non-local theories suggested by <a href="/wiki/Anthony_Leggett" class="mw-redirect" title="Anthony Leggett">Anthony Leggett</a> is ruled out. Based on this, the authors conclude that any possible <a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">non-local</a> <a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">hidden-variable theory</a> consistent with quantum mechanics must be highly counterintuitive.<sup id="cite_ref-quantum_22-0" class="reference"><a href="#cite_note-quantum-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-quantum2_23-0" class="reference"><a href="#cite_note-quantum2-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Salart_et_al._(2008):_separation_in_a_Bell_Test"><span id="Salart_et_al._.282008.29:_separation_in_a_Bell_Test"></span>Salart et al. (2008): separation in a Bell Test</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=16" title="Edit section: Salart et al. (2008): separation in a Bell Test"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This experiment filled a loophole by providing an 18 km separation between detectors, which is sufficient to allow the completion of the quantum state measurements before any information could have traveled between the two detectors.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Ansmann_et_al._(2009):_overcoming_the_detection_loophole_in_solid_state"><span id="Ansmann_et_al._.282009.29:_overcoming_the_detection_loophole_in_solid_state"></span>Ansmann et al. (2009): overcoming the detection loophole in solid state</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=17" title="Edit section: Ansmann et al. (2009): overcoming the detection loophole in solid state"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This was the first experiment testing Bell inequalities with solid-state qubits (superconducting <a href="/wiki/Phase_qubit" title="Phase qubit">Josephson phase qubits</a> were used). This experiment surmounted the detection loophole using a pair of superconducting qubits in an entangled state. However, the experiment still suffered from the locality loophole because the qubits were only separated by a few millimeters.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Giustina_et_al._(2013),_Larsson_et_al_(2014):_overcoming_the_detection_loophole_for_photons"><span id="Giustina_et_al._.282013.29.2C_Larsson_et_al_.282014.29:_overcoming_the_detection_loophole_for_photons"></span><a href="/wiki/Marissa_Giustina" title="Marissa Giustina">Giustina</a> et al. (2013), Larsson et al (2014): overcoming the detection loophole for photons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=18" title="Edit section: Giustina et al. (2013), Larsson et al (2014): overcoming the detection loophole for photons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The detection loophole for photons has been closed for the first time by <a href="/wiki/Marissa_Giustina" title="Marissa Giustina">Marissa Giustina</a>, using <a href="/wiki/Transition_edge_sensor" class="mw-redirect" title="Transition edge sensor">highly efficient detectors</a>. This makes photons the first system for which all of the main loopholes have been closed, albeit in different experiments.<sup id="cite_ref-giustina_27-0" class="reference"><a href="#cite_note-giustina-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-larsson_28-0" class="reference"><a href="#cite_note-larsson-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Christensen_et_al._(2013):_overcoming_the_detection_loophole_for_photons"><span id="Christensen_et_al._.282013.29:_overcoming_the_detection_loophole_for_photons"></span>Christensen et al. (2013): overcoming the detection loophole for photons</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=19" title="Edit section: Christensen et al. (2013): overcoming the detection loophole for photons"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Christensen et al. (2013)<sup id="cite_ref-christensen_29-0" class="reference"><a href="#cite_note-christensen-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> experiment is similar to that of Giustina et al.<sup id="cite_ref-giustina_27-1" class="reference"><a href="#cite_note-giustina-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> Giustina et al. did just four long runs with constant measurement settings (one for each of the four pairs of settings). The experiment was not pulsed so that formation of "pairs" from the two records of measurement results (Alice and Bob) had to be done after the experiment which in fact exposes the experiment to the coincidence loophole. This led to a reanalysis of the experimental data in a way which removed the coincidence loophole, and fortunately the new analysis still showed a violation of the appropriate CHSH or CH inequality.<sup id="cite_ref-larsson_28-1" class="reference"><a href="#cite_note-larsson-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> On the other hand, the Christensen et al. experiment was pulsed and measurement settings were frequently reset in a random way, though only once every 1000 particle pairs, not every time.<sup id="cite_ref-christensen_29-1" class="reference"><a href="#cite_note-christensen-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Hensen_et_al.,_Giustina_et_al.,_Shalm_et_al._(2015):_"loophole-free"_Bell_tests"><span id="Hensen_et_al..2C_Giustina_et_al..2C_Shalm_et_al._.282015.29:_.22loophole-free.22_Bell_tests"></span>Hensen et al., Giustina et al., Shalm et al. (2015): "loophole-free" Bell tests</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=20" title="Edit section: Hensen et al., Giustina et al., Shalm et al. (2015): "loophole-free" Bell tests"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2015 the first three significant-loophole-free Bell-tests were published within three months by independent groups in Delft, Vienna and Boulder. All three tests simultaneously addressed the detection loophole, the locality loophole, and the memory loophole. This makes them “loophole-free” in the sense that all remaining conceivable loopholes like <a href="/wiki/Superdeterminism" title="Superdeterminism">superdeterminism</a> require truly exotic hypotheses that might never get closed experimentally. </p><p>The first published experiment by Hensen et al.<sup id="cite_ref-Hensen_et_al._10-1" class="reference"><a href="#cite_note-Hensen_et_al.-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> used a photonic link to entangle the <a href="/wiki/Electron_magnetic_moment" title="Electron magnetic moment">electron spins</a> of two <a href="/wiki/Nitrogen-vacancy_center" title="Nitrogen-vacancy center">nitrogen-vacancy</a> defect centres in diamonds 1.3 kilometers apart and measured a violation of the CHSH inequality (<i>S</i> = 2.42 ± 0.20). Thereby the local-realist hypothesis could be rejected with a <a href="/wiki/P-value" title="P-value"><i>p</i>-value</a> of 0.039. </p><p>Both simultaneously published experiments by Giustina et al.<sup id="cite_ref-Zeilinger-2015_30-0" class="reference"><a href="#cite_note-Zeilinger-2015-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> and Shalm et al.<sup id="cite_ref-Kwiat-2015_31-0" class="reference"><a href="#cite_note-Kwiat-2015-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> used entangled photons to obtain a Bell inequality violation with high statistical significance (p-value ≪10<sup>−6</sup>). Notably, the experiment by Shalm et al. also combined three types of (quasi-)random number generators to determine the measurement basis choices. One of these methods, detailed in an ancillary file, is the “'Cultural' <a href="/wiki/Pseudorandom_number_generator" title="Pseudorandom number generator">pseudorandom</a> source” which involved using bit strings from popular media such as the <a href="/wiki/Back_to_the_Future_(franchise)" title="Back to the Future (franchise)"><i>Back to the Future</i> films</a>, <i><a href="/wiki/Star_Trek:_Beyond_the_Final_Frontier" title="Star Trek: Beyond the Final Frontier">Star Trek: Beyond the Final Frontier</a></i>, <i><a href="/wiki/Monty_Python_and_the_Holy_Grail" title="Monty Python and the Holy Grail">Monty Python and the Holy Grail</a></i>, and the television shows <i><a href="/wiki/Saved_by_the_Bell" title="Saved by the Bell">Saved by the Bell</a></i> and <i><a href="/wiki/Doctor_Who" title="Doctor Who">Dr. Who</a></i>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Schmied_et_al._(2016):_Detection_of_Bell_correlations_in_a_many-body_system"><span id="Schmied_et_al._.282016.29:_Detection_of_Bell_correlations_in_a_many-body_system"></span>Schmied et al. (2016): Detection of Bell correlations in a many-body system</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=21" title="Edit section: Schmied et al. (2016): Detection of Bell correlations in a many-body system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Using a witness for Bell correlations derived from a multi-partite Bell inequality, physicists at the <a href="/wiki/University_of_Basel" title="University of Basel">University of Basel</a> were able to conclude for the first time Bell correlation in a many-body system composed by about 480 atoms in a <a href="/wiki/Bose%E2%80%93Einstein_condensate" title="Bose–Einstein condensate">Bose–Einstein condensate</a>. Even though loopholes were not closed, this experiment shows the possibility of observing Bell correlations in the macroscopic regime.<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Handsteiner_et_al._(2017):_"Cosmic_Bell_Test"_-_Measurement_Settings_from_Milky_Way_Stars"><span id="Handsteiner_et_al._.282017.29:_.22Cosmic_Bell_Test.22_-_Measurement_Settings_from_Milky_Way_Stars"></span>Handsteiner et al. (2017): "Cosmic Bell Test" - Measurement Settings from Milky Way Stars</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=22" title="Edit section: Handsteiner et al. (2017): "Cosmic Bell Test" - Measurement Settings from Milky Way Stars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Physicists led by <a href="/wiki/David_Kaiser_(physicist)" title="David Kaiser (physicist)">David Kaiser</a> of the <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a> and Anton Zeilinger of the <a href="/wiki/Institute_for_Quantum_Optics_and_Quantum_Information" title="Institute for Quantum Optics and Quantum Information">Institute for Quantum Optics and Quantum Information</a> and <a href="/wiki/University_of_Vienna" title="University of Vienna">University of Vienna</a> performed an experiment that "produced results consistent with nonlocality" by measuring starlight that had taken 600 years to travel to Earth.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> The experiment “represents the first experiment to dramatically limit the space-time region in which hidden variables could be relevant.”<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Rosenfeld_et_al._(2017):_"Event-Ready"_Bell_test_with_entangled_atoms_and_closed_detection_and_locality_loopholes"><span id="Rosenfeld_et_al._.282017.29:_.22Event-Ready.22_Bell_test_with_entangled_atoms_and_closed_detection_and_locality_loopholes"></span>Rosenfeld et al. (2017): "Event-Ready" Bell test with entangled atoms and closed detection and locality loopholes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=23" title="Edit section: Rosenfeld et al. (2017): "Event-Ready" Bell test with entangled atoms and closed detection and locality loopholes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Physicists at the <a href="/wiki/Ludwig_Maximilian_University_of_Munich" title="Ludwig Maximilian University of Munich">Ludwig Maximilian University of Munich</a> and the <a href="/wiki/Max_Planck_Institute_of_Quantum_Optics" title="Max Planck Institute of Quantum Optics">Max Planck Institute of Quantum Optics</a> published results from an experiment in which they observed a Bell inequality violation using entangled spin states of two atoms with a separation distance of 398 meters in which the detection loophole, the locality loophole, and the memory loophole were closed. The violation of S = 2.221 ± 0.033 rejected local realism with a significance value of P = 1.02×10<sup>−16</sup> when taking into account 7 months of data and 55000 events or an upper bound of P = 2.57×10<sup>−9</sup> from a single run with 10000 events.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="The_BIG_Bell_Test_Collaboration_(2018):_“Challenging_local_realism_with_human_choices”"><span id="The_BIG_Bell_Test_Collaboration_.282018.29:_.E2.80.9CChallenging_local_realism_with_human_choices.E2.80.9D"></span>The BIG Bell Test Collaboration (2018): “Challenging local realism with human choices”</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=24" title="Edit section: The BIG Bell Test Collaboration (2018): “Challenging local realism with human choices”"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An international collaborative scientific effort used arbitrary human choice to define measurement settings instead of using random number generators. Assuming that human free will exists, this would close the “freedom-of-choice loophole”. Around 100,000 participants were recruited in order to provide sufficient input for the experiment to be statistically significant.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Rauch_et_al_(2018):_measurement_settings_from_distant_quasars"><span id="Rauch_et_al_.282018.29:_measurement_settings_from_distant_quasars"></span>Rauch et al (2018): measurement settings from distant quasars</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=25" title="Edit section: Rauch et al (2018): measurement settings from distant quasars"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2018, an international team used light from two <a href="/wiki/Quasar" title="Quasar">quasars</a> (one whose light was generated approximately eight billion years ago and the other approximately twelve billion years ago) as the basis for their measurement settings.<sup id="cite_ref-Hamish_2018_40-0" class="reference"><a href="#cite_note-Hamish_2018-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> This experiment pushed the timeframe for when the settings could have been mutually determined to at least 7.8 billion years in the past, a substantial fraction of the <a href="/wiki/Superdeterminism" title="Superdeterminism">superdeterministic</a> limit (that being the <a href="/wiki/Big_Bang" title="Big Bang">creation of the universe</a> 13.8 billion years ago).<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p><p>The 2019 <a href="/wiki/PBS_Nova" class="mw-redirect" title="PBS Nova">PBS Nova</a> episode <i>Einstein's Quantum Riddle</i> documents this "cosmic Bell test" measurement, with footage of the scientific team on-site at the high-altitude <a href="/wiki/Teide_Observatory" title="Teide Observatory">Teide Observatory</a> located in the <a href="/wiki/Canary_Islands" title="Canary Islands">Canary Islands</a>.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Storz_et_al_(2023):_Loophole-free_Bell_inequality_violation_with_superconducting_circuits"><span id="Storz_et_al_.282023.29:_Loophole-free_Bell_inequality_violation_with_superconducting_circuits"></span>Storz et al (2023): Loophole-free Bell inequality violation with superconducting circuits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=26" title="Edit section: Storz et al (2023): Loophole-free Bell inequality violation with superconducting circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2023, an international team led by the group of <a href="/wiki/Andreas_Wallraff" title="Andreas Wallraff">Andreas Wallraff</a> at <a href="/wiki/ETH_Zurich" title="ETH Zurich">ETH Zurich</a> demonstrated a loophole-free violation of the <a href="/wiki/CHSH_inequality" title="CHSH inequality">CHSH inequality</a> with superconducting circuits deterministically entangled via a cryogenic link spanning a distance of 30 meters.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Loopholes">Loopholes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=27" title="Edit section: Loopholes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Though the series of increasingly sophisticated Bell test experiments has convinced the physics community that local hidden-variable theories are indefensible; they can never be excluded entirely.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> For example, the hypothesis of <a href="/wiki/Superdeterminism" title="Superdeterminism">superdeterminism</a> in which all experiments and outcomes (and everything else) are predetermined can never be excluded (because it is <a href="/wiki/Falsifiability" title="Falsifiability">unfalsifiable</a>).<sup id="cite_ref-larsson14_45-0" class="reference"><a href="#cite_note-larsson14-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p><p>Up to 2015, the outcome of all experiments that violate a Bell inequality could still theoretically be explained by exploiting the detection loophole and/or the locality loophole. The locality (or communication) loophole means that since in actual practice the two detections are separated by a <a href="/wiki/Spacetime#Time-like_interval" title="Spacetime">time-like interval</a>, the first detection may influence the second by some kind of signal. To avoid this loophole, the experimenter has to ensure that particles travel far apart before being measured, and that the measurement process is rapid. More serious is the detection (or unfair sampling) loophole, because particles are not always detected in both wings of the experiment. It can be imagined that the complete set of particles would behave randomly, but instruments only detect a subsample showing <a href="/wiki/Quantum_correlation" title="Quantum correlation">quantum correlations</a>, by letting detection be dependent on a combination of local hidden variables and detector setting.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2022)">citation needed</span></a></i>]</sup> </p><p>Experimenters had repeatedly voiced that loophole-free tests could be expected in the near future.<sup id="cite_ref-García-Patrón-2004_46-0" class="reference"><a href="#cite_note-García-Patrón-2004-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gill-2003_47-0" class="reference"><a href="#cite_note-Gill-2003-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> In 2015, a loophole-free Bell violation was reported using entangled diamond spins over a distance of 1.3 kilometres (1,300 m)<sup id="cite_ref-Hensen_et_al._10-2" class="reference"><a href="#cite_note-Hensen_et_al.-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> and corroborated by two experiments using entangled photon pairs.<sup id="cite_ref-Zeilinger-2015_30-1" class="reference"><a href="#cite_note-Zeilinger-2015-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kwiat-2015_31-1" class="reference"><a href="#cite_note-Kwiat-2015-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p><p>The remaining possible theories that obey local realism can be further restricted by testing different spatial configurations, methods to determine the measurement settings, and recording devices. It has been suggested that using humans to generate the measurement settings and observe the outcomes provides a further test.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> David Kaiser of <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">MIT</a> told the <i>New York Times</i> in 2015 that a potential weakness of the "loophole-free" experiments is that the systems used to add randomness to the measurement may be predetermined in a method that was not detected in experiments.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Detection_loophole">Detection loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=28" title="Edit section: Detection loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A common problem in optical Bell tests is that only a small fraction of the emitted photons are detected. It is then possible that the correlations of the detected photons are unrepresentative: although they show a violation of a Bell inequality, if all photons were detected the Bell inequality would actually be respected. This was first noted by Philip M. Pearle in 1970,<sup id="cite_ref-Pearle-1970_50-0" class="reference"><a href="#cite_note-Pearle-1970-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> who devised a local hidden variable model that faked a Bell violation by letting the photon be detected only if the measurement setting was favourable. The assumption that this does not happen, i.e., that the small sample is actually representative of the whole is called the <i>fair sampling</i> assumption. </p><p>To do away with this assumption it is necessary to detect a sufficiently large fraction of the photons. This is usually characterized in terms of the detection efficiency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e4d701857cf5fbec133eebaf94deadf722537f64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.169ex; height:2.176ex;" alt="{\displaystyle \eta }"></span>, defined as the probability that a photodetector detects a photon that arrives at it. <a href="/wiki/Anupam_Garg" title="Anupam Garg">Anupam Garg</a> and <a href="/wiki/N._David_Mermin" title="N. David Mermin">N. David Mermin</a> showed that when using a maximally entangled state and the CHSH inequality an efficiency of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta >2{\sqrt {2}}-2\approx 0.83}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>></mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>−</mo> <mn>2</mn> <mo>≈</mo> <mn>0.83</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta >2{\sqrt {2}}-2\approx 0.83}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/182e2247014bf390f2e1fd0d3e7643ca3f9adea4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.764ex; height:3.176ex;" alt="{\displaystyle \eta >2{\sqrt {2}}-2\approx 0.83}"></span> is required for a loophole-free violation.<sup id="cite_ref-Garg_&_Mermin,_1987_51-0" class="reference"><a href="#cite_note-Garg_&_Mermin,_1987-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> Later Philippe H. Eberhard showed that when using a <i>partially</i> entangled state a loophole-free violation is possible for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta >2/3\approx 0.67}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>></mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> <mo>≈</mo> <mn>0.67</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta >2/3\approx 0.67}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1930eb709210bb391da49fbcf6fb6f86ee361994" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.988ex; height:2.843ex;" alt="{\displaystyle \eta >2/3\approx 0.67}"></span>,<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> which is the optimal bound for the CHSH inequality.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> Other Bell inequalities allow for even lower bounds. For example, there exists a four-setting inequality which is violated for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta >({\sqrt {5}}-1)/2\approx 0.62}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>η</mi> <mo>></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo>≈</mo> <mn>0.62</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \eta >({\sqrt {5}}-1)/2\approx 0.62}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/551901e05fc469ba5354f8b218de6a4561e7c1ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.736ex; height:3.009ex;" alt="{\displaystyle \eta >({\sqrt {5}}-1)/2\approx 0.62}"></span>.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> </p><p>Historically, only experiments with non-optical systems have been able to reach high enough efficiencies to close this loophole, such as trapped ions,<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> superconducting qubits,<sup id="cite_ref-Ansmann_56-0" class="reference"><a href="#cite_note-Ansmann-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Nitrogen-vacancy_center" title="Nitrogen-vacancy center">nitrogen-vacancy centers</a>.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> These experiments were not able to close the locality loophole, which is easy to do with photons. More recently, however, optical setups have managed to reach sufficiently high detection efficiencies by using superconducting photodetectors,<sup id="cite_ref-Zeilinger-2015_30-2" class="reference"><a href="#cite_note-Zeilinger-2015-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Kwiat-2015_31-2" class="reference"><a href="#cite_note-Kwiat-2015-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> and hybrid setups have managed to combine the high detection efficiency typical of matter systems with the ease of distributing entanglement at a distance typical of photonic systems.<sup id="cite_ref-Hensen_et_al._10-3" class="reference"><a href="#cite_note-Hensen_et_al.-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Locality_loophole">Locality loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=29" title="Edit section: Locality loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>One of the assumptions of Bell's theorem is the one of locality, namely that the choice of setting at a measurement site does not influence the result of the other. The motivation for this assumption is the <a href="/wiki/Special_relativity" title="Special relativity">theory of relativity</a>, that prohibits communication faster than light. For this motivation to apply to an experiment, it needs to have space-like separation between its measurements events. That is, the time that passes between the choice of measurement setting and the production of an outcome must be shorter than the time it takes for a light signal to travel between the measurement sites.<sup id="cite_ref-Bell-1987b_58-0" class="reference"><a href="#cite_note-Bell-1987b-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> </p><p>The first experiment that strived to respect this condition was Aspect's 1982 experiment.<sup id="cite_ref-Aspect-1982b_15-1" class="reference"><a href="#cite_note-Aspect-1982b-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In it the settings were changed fast enough, but deterministically. The first experiment to change the settings randomly, with the choices made by a <a href="/wiki/Quantum_random_number_generator" class="mw-redirect" title="Quantum random number generator">quantum random number generator</a>, was Weihs et al.'s 1998 experiment.<sup id="cite_ref-Weihs-1998_18-1" class="reference"><a href="#cite_note-Weihs-1998-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> Scheidl et al. improved on this further in 2010 by conducting an experiment between locations separated by a distance of 144 km (89 mi).<sup id="cite_ref-Scheidl-2010_59-0" class="reference"><a href="#cite_note-Scheidl-2010-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Coincidence_loophole">Coincidence loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=30" title="Edit section: Coincidence loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In many experiments, especially those based on photon polarization, pairs of events in the two wings of the experiment are only identified as belonging to a single pair after the experiment is performed, by judging whether or not their detection times are close enough to one another. This generates a new possibility for a local hidden variables theory to "fake" quantum correlations: delay the detection time of each of the two particles by a larger or smaller amount depending on some relationship between hidden variables carried by the particles and the detector settings encountered at the measurement station.<sup id="cite_ref-Larsson2004_60-0" class="reference"><a href="#cite_note-Larsson2004-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p><p>The coincidence loophole can be ruled out entirely simply by working with a pre-fixed lattice of detection windows which are short enough that most pairs of events occurring in the same window do originate with the same emission and long enough that a true pair is not separated by a window boundary.<sup id="cite_ref-Larsson2004_60-1" class="reference"><a href="#cite_note-Larsson2004-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Memory_loophole">Memory loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=31" title="Edit section: Memory loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In most experiments, measurements are repeatedly made at the same two locations. A local hidden variable theory could exploit the memory of past measurement settings and outcomes in order to increase the violation of a Bell inequality. Moreover, physical parameters might be varying in time. It has been shown that, provided each new pair of measurements is done with a new random pair of measurement settings, that neither memory nor time inhomogeneity have a serious effect on the experiment.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gill2002_63-0" class="reference"><a href="#cite_note-Gill2002-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Superdeterminism">Superdeterminism</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=32" title="Edit section: Superdeterminism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></div> <p>A necessary assumption to derive Bell's theorem is that the hidden variables are not correlated with the measurement settings. This assumption has been justified on the grounds that the experimenter has "<a href="/wiki/Free_will" title="Free will">free will</a>" to choose the settings, and that such is necessary to do science in the first place. A (hypothetical) theory where the choice of measurement is determined by the system being measured is known as <i>superdeterministic</i>.<sup id="cite_ref-larsson14_45-1" class="reference"><a href="#cite_note-larsson14-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Many-worlds_loophole">Many-worlds loophole</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=33" title="Edit section: Many-worlds loophole"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">many-worlds interpretation</a>, also known as the <a href="/wiki/Hugh_Everett_III" title="Hugh Everett III">Hugh Everett</a> interpretation, is deterministic and has local dynamics, consisting of the unitary part of quantum mechanics without collapse. Bell's theorem does not apply because of an implicit assumption that measurements have a single outcome.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=34" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Determinism" title="Determinism">Determinism</a> – <a href="/wiki/Determinism#Quantum_and_classical_mechanics" title="Determinism">Quantum and classical mechanics</a></li> <li><a href="/wiki/Einstein%27s_thought_experiments" title="Einstein's thought experiments">Einstein's thought experiments</a></li> <li><a href="/wiki/Principle_of_locality" title="Principle of locality">Principle of locality</a></li> <li><a href="/wiki/Quantum_indeterminacy" title="Quantum indeterminacy">Quantum indeterminacy</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Bell_test&action=edit&section=35" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-Markoff-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Markoff_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Markoff_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output 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(2003). "Accardi contra Bell (cum mundi): The Impossible Coupling". In M. Moore; S. Froda; C. Léger (eds.). <i>Mathematical Statistics and Applications: Festschrift for Constance van Eeden</i>. IMS Lecture Notes — Monograph Series. Vol. 42. 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(2002). "Time, Finite Statistics, and Bell's Fifth Position". <i>Proceedings of the Conference Foundations of Probability and Physics - 2 : Växjö (Soland), Sweden, June 2-7, 2002</i>. Vol. 5. 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A</i>. <b>66</b> (4): 042111. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0205016">quant-ph/0205016</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2002PhRvA..66d2111B">2002PhRvA..66d2111B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.66.042111">10.1103/PhysRevA.66.042111</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:6524446">6524446</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+A&rft.atitle=Quantum+Nonlocality%2C+Bell+Inequalities+and+the+Memory+Loophole&rft.volume=66&rft.issue=4&rft.pages=042111&rft.date=2002&rft_id=info%3Aarxiv%2Fquant-ph%2F0205016&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A6524446%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.66.042111&rft_id=info%3Abibcode%2F2002PhRvA..66d2111B&rft.au=J.+Barrett&rft.au=D.+Collins&rft.au=L.+Hardy&rft.au=A.+Kent&rft.au=S.+Popescu&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABell+test" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJ._S._Bell1987" class="citation book cs1">J. S. Bell (1987). <i>Speakable and Unspeakable in Quantum Mechanics</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-33495-2" title="Special:BookSources/978-0-521-33495-2"><bdi>978-0-521-33495-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Speakable+and+Unspeakable+in+Quantum+Mechanics&rft.pub=Cambridge+University+Press&rft.date=1987&rft.isbn=978-0-521-33495-2&rft.au=J.+S.+Bell&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABell+test" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFD._KielpinskiA._Ben-KishJ._BrittonV._Meyer2001" class="citation arxiv cs1">D. Kielpinski; A. Ben-Kish; J. Britton; V. Meyer; M.A. Rowe; C.A. Sackett; W.M. Itano; C. Monroe; D.J. Wineland (2001). "Recent Results in Trapped-Ion Quantum Computing". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/0102086">quant-ph/0102086</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=Recent+Results+in+Trapped-Ion+Quantum+Computing&rft.date=2001&rft_id=info%3Aarxiv%2Fquant-ph%2F0102086&rft.au=D.+Kielpinski&rft.au=A.+Ben-Kish&rft.au=J.+Britton&rft.au=V.+Meyer&rft.au=M.A.+Rowe&rft.au=C.A.+Sackett&rft.au=W.M.+Itano&rft.au=C.+Monroe&rft.au=D.J.+Wineland&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABell+test" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFP.G._KwiatE._WaksA.G._WhiteI._Appelbaum1999" class="citation journal cs1">P.G. Kwiat; E. Waks; A.G. White; I. Appelbaum; P.H. Eberhard (1999). "Ultrabright source of polarization-entangled photons". <i>Physical Review A</i>. <b>60</b> (2): R773–6. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/quant-ph/9810003">quant-ph/9810003</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999PhRvA..60..773K">1999PhRvA..60..773K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevA.60.R773">10.1103/PhysRevA.60.R773</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:16417960">16417960</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+A&rft.atitle=Ultrabright+source+of+polarization-entangled+photons&rft.volume=60&rft.issue=2&rft.pages=R773-6&rft.date=1999&rft_id=info%3Aarxiv%2Fquant-ph%2F9810003&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A16417960%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1103%2FPhysRevA.60.R773&rft_id=info%3Abibcode%2F1999PhRvA..60..773K&rft.au=P.G.+Kwiat&rft.au=E.+Waks&rft.au=A.G.+White&rft.au=I.+Appelbaum&rft.au=P.H.+Eberhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABell+test" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid 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.navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Quantum_mechanics332" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Quantum_mechanics_topics" title="Template:Quantum mechanics topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Quantum_mechanics_topics" title="Template talk:Quantum mechanics topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Quantum_mechanics_topics" title="Special:EditPage/Template:Quantum mechanics topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Quantum_mechanics332" style="font-size:114%;margin:0 4em"><a href="/wiki/Quantum_mechanics" title="Quantum mechanics">Quantum mechanics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Background</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Introduction_to_quantum_mechanics" title="Introduction to quantum mechanics">Introduction</a></li> <li><a href="/wiki/History_of_quantum_mechanics" title="History of quantum mechanics">History</a> <ul><li><a href="/wiki/Timeline_of_quantum_mechanics" title="Timeline of quantum mechanics">Timeline</a></li></ul></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Old_quantum_theory" title="Old quantum theory">Old quantum theory</a></li> <li><a href="/wiki/Glossary_of_elementary_quantum_mechanics" title="Glossary of elementary quantum mechanics">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Fundamentals</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Born_rule" title="Born rule">Born rule</a></li> <li><a href="/wiki/Bra%E2%80%93ket_notation" title="Bra–ket notation">Bra–ket notation</a></li> <li><a href="/wiki/Complementarity_(physics)" title="Complementarity (physics)"> Complementarity</a></li> <li><a href="/wiki/Density_matrix" title="Density matrix">Density matrix</a></li> <li><a href="/wiki/Energy_level" title="Energy level">Energy level</a> <ul><li><a href="/wiki/Ground_state" title="Ground state">Ground state</a></li> <li><a href="/wiki/Excited_state" title="Excited state">Excited state</a></li> <li><a href="/wiki/Degenerate_energy_levels" title="Degenerate energy levels">Degenerate levels</a></li> <li><a href="/wiki/Zero-point_energy" title="Zero-point energy">Zero-point energy</a></li></ul></li> <li><a href="/wiki/Quantum_entanglement" title="Quantum entanglement">Entanglement</a></li> <li><a href="/wiki/Hamiltonian_(quantum_mechanics)" title="Hamiltonian (quantum mechanics)">Hamiltonian</a></li> <li><a href="/wiki/Wave_interference" title="Wave interference">Interference</a></li> <li><a href="/wiki/Quantum_decoherence" title="Quantum decoherence">Decoherence</a></li> <li><a href="/wiki/Measurement_in_quantum_mechanics" title="Measurement in quantum mechanics">Measurement</a></li> <li><a href="/wiki/Quantum_nonlocality" title="Quantum nonlocality">Nonlocality</a></li> <li><a href="/wiki/Quantum_state" title="Quantum state">Quantum state</a></li> <li><a href="/wiki/Quantum_superposition" title="Quantum superposition">Superposition</a></li> <li><a href="/wiki/Quantum_tunnelling" title="Quantum tunnelling">Tunnelling</a></li> <li><a href="/wiki/Scattering_theory" class="mw-redirect" title="Scattering theory">Scattering theory</a></li> <li><a href="/wiki/Symmetry_in_quantum_mechanics" title="Symmetry in quantum mechanics">Symmetry in quantum mechanics</a></li> <li><a href="/wiki/Uncertainty_principle" title="Uncertainty principle">Uncertainty</a></li> <li><a href="/wiki/Wave_function" title="Wave function">Wave function</a> <ul><li><a href="/wiki/Wave_function_collapse" title="Wave function collapse">Collapse</a></li> <li><a href="/wiki/Wave%E2%80%93particle_duality" title="Wave–particle duality">Wave–particle duality</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formulations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematical_formulation_of_quantum_mechanics" title="Mathematical formulation of quantum mechanics">Formulations</a></li> <li><a href="/wiki/Heisenberg_picture" title="Heisenberg picture">Heisenberg</a></li> <li><a href="/wiki/Interaction_picture" title="Interaction picture">Interaction</a></li> <li><a href="/wiki/Matrix_mechanics" title="Matrix mechanics">Matrix mechanics</a></li> <li><a href="/wiki/Schr%C3%B6dinger_picture" title="Schrödinger picture">Schrödinger</a></li> <li><a href="/wiki/Path_integral_formulation" title="Path integral formulation">Path integral formulation</a></li> <li><a href="/wiki/Phase-space_formulation" title="Phase-space formulation">Phase space</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Equations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Klein%E2%80%93Gordon_equation" title="Klein–Gordon equation">Klein–Gordon</a></li> <li><a href="/wiki/Dirac_equation" title="Dirac equation">Dirac</a></li> <li><a href="/wiki/Weyl_equation" title="Weyl equation">Weyl</a></li> <li><a href="/wiki/Majorana_equation" title="Majorana equation">Majorana</a></li> <li><a href="/wiki/Rarita%E2%80%93Schwinger_equation" title="Rarita–Schwinger equation">Rarita–Schwinger</a></li> <li><a href="/wiki/Pauli_equation" title="Pauli equation">Pauli</a></li> <li><a href="/wiki/Rydberg_formula" title="Rydberg formula">Rydberg</a></li> <li><a href="/wiki/Schr%C3%B6dinger_equation" title="Schrödinger equation">Schrödinger</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_Bayesianism" title="Quantum Bayesianism">Bayesian</a></li> <li><a href="/wiki/Consistent_histories" title="Consistent histories">Consistent histories</a></li> <li><a href="/wiki/Copenhagen_interpretation" title="Copenhagen interpretation">Copenhagen</a></li> <li><a href="/wiki/De_Broglie%E2%80%93Bohm_theory" title="De Broglie–Bohm theory">de Broglie–Bohm</a></li> <li><a href="/wiki/Ensemble_interpretation" title="Ensemble interpretation">Ensemble</a></li> <li><a href="/wiki/Hidden-variable_theory" title="Hidden-variable theory">Hidden-variable</a> <ul><li><a href="/wiki/Local_hidden-variable_theory" title="Local hidden-variable theory">Local</a> <ul><li><a href="/wiki/Superdeterminism" title="Superdeterminism">Superdeterminism</a></li></ul></li></ul></li> <li><a href="/wiki/Many-worlds_interpretation" title="Many-worlds interpretation">Many-worlds</a></li> <li><a href="/wiki/Objective-collapse_theory" title="Objective-collapse theory">Objective collapse</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Relational_quantum_mechanics" title="Relational quantum mechanics">Relational</a></li> <li><a href="/wiki/Transactional_interpretation" title="Transactional interpretation">Transactional</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Wigner_interpretation" title="Von Neumann–Wigner interpretation">Von Neumann–Wigner</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Experiments</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Bell test</a></li> <li><a href="/wiki/Davisson%E2%80%93Germer_experiment" title="Davisson–Germer experiment">Davisson–Germer</a></li> <li><a href="/wiki/Delayed-choice_quantum_eraser" title="Delayed-choice quantum eraser">Delayed-choice quantum eraser</a></li> <li><a href="/wiki/Double-slit_experiment" title="Double-slit experiment">Double-slit</a></li> <li><a href="/wiki/Franck%E2%80%93Hertz_experiment" title="Franck–Hertz experiment">Franck–Hertz</a></li> <li><a href="/wiki/Mach%E2%80%93Zehnder_interferometer" title="Mach–Zehnder interferometer">Mach–Zehnder interferometer</a></li> <li><a href="/wiki/Elitzur%E2%80%93Vaidman_bomb_tester" title="Elitzur–Vaidman bomb tester">Elitzur–Vaidman</a></li> <li><a href="/wiki/Popper%27s_experiment" title="Popper's experiment">Popper</a></li> <li><a href="/wiki/Quantum_eraser_experiment" title="Quantum eraser experiment">Quantum eraser</a></li> <li><a href="/wiki/Stern%E2%80%93Gerlach_experiment" title="Stern–Gerlach experiment">Stern–Gerlach</a></li> <li><a href="/wiki/Wheeler%27s_delayed-choice_experiment" title="Wheeler's delayed-choice experiment">Wheeler's delayed choice</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_nanoscience" class="mw-redirect" title="Quantum nanoscience">Science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_biology" title="Quantum biology">Quantum biology</a></li> <li><a href="/wiki/Quantum_chemistry" title="Quantum chemistry">Quantum chemistry</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Quantum_cosmology" title="Quantum cosmology">Quantum cosmology</a></li> <li><a href="/wiki/Quantum_differential_calculus" title="Quantum differential calculus">Quantum differential calculus</a></li> <li><a href="/wiki/Quantum_dynamics" title="Quantum dynamics">Quantum dynamics</a></li> <li><a href="/wiki/Quantum_geometry" title="Quantum geometry">Quantum geometry</a></li> <li><a href="/wiki/Measurement_problem" title="Measurement problem">Quantum measurement problem</a></li> <li><a href="/wiki/Quantum_mind" title="Quantum mind">Quantum mind</a></li> <li><a href="/wiki/Quantum_stochastic_calculus" title="Quantum stochastic calculus">Quantum stochastic calculus</a></li> <li><a href="/wiki/Quantum_spacetime" title="Quantum spacetime">Quantum spacetime</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Quantum_technology" class="mw-redirect" title="Quantum technology">Technology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_algorithm" title="Quantum algorithm">Quantum algorithms</a></li> <li><a href="/wiki/Quantum_amplifier" title="Quantum amplifier">Quantum amplifier</a></li> <li><a href="/wiki/Quantum_bus" title="Quantum bus">Quantum bus</a></li> <li><a href="/wiki/Quantum_cellular_automaton" title="Quantum cellular automaton">Quantum cellular automata</a> <ul><li><a href="/wiki/Quantum_finite_automaton" title="Quantum finite automaton">Quantum finite automata</a></li></ul></li> <li><a href="/wiki/Quantum_channel" title="Quantum channel">Quantum channel</a></li> <li><a href="/wiki/Quantum_circuit" title="Quantum circuit">Quantum circuit</a></li> <li><a href="/wiki/Quantum_complexity_theory" title="Quantum complexity theory">Quantum complexity theory</a></li> <li><a href="/wiki/Quantum_computing" title="Quantum computing">Quantum computing</a> <ul><li><a href="/wiki/Timeline_of_quantum_computing_and_communication" title="Timeline of quantum computing and communication">Timeline</a></li></ul></li> <li><a href="/wiki/Quantum_cryptography" title="Quantum cryptography">Quantum cryptography</a></li> <li><a href="/wiki/Quantum_electronics" class="mw-redirect" title="Quantum electronics">Quantum electronics</a></li> <li><a href="/wiki/Quantum_error_correction" title="Quantum error correction">Quantum error correction</a></li> <li><a href="/wiki/Quantum_imaging" title="Quantum imaging">Quantum imaging</a></li> <li><a href="/wiki/Quantum_image_processing" title="Quantum image processing">Quantum image processing</a></li> <li><a href="/wiki/Quantum_information" title="Quantum information">Quantum information</a></li> <li><a href="/wiki/Quantum_key_distribution" title="Quantum key distribution">Quantum key distribution</a></li> <li><a href="/wiki/Quantum_logic" title="Quantum logic">Quantum logic</a></li> <li><a href="/wiki/Quantum_logic_gate" title="Quantum logic gate">Quantum logic gates</a></li> <li><a href="/wiki/Quantum_machine" title="Quantum machine">Quantum machine</a></li> <li><a href="/wiki/Quantum_machine_learning" title="Quantum machine learning">Quantum machine learning</a></li> <li><a href="/wiki/Quantum_metamaterial" title="Quantum metamaterial">Quantum metamaterial</a></li> <li><a href="/wiki/Quantum_metrology" title="Quantum metrology">Quantum metrology</a></li> <li><a href="/wiki/Quantum_network" title="Quantum network">Quantum network</a></li> <li><a href="/wiki/Quantum_neural_network" title="Quantum neural network">Quantum neural network</a></li> <li><a href="/wiki/Quantum_optics" title="Quantum optics">Quantum optics</a></li> <li><a href="/wiki/Quantum_programming" title="Quantum programming">Quantum programming</a></li> <li><a href="/wiki/Quantum_sensor" title="Quantum sensor">Quantum sensing</a></li> <li><a href="/wiki/Quantum_simulator" title="Quantum simulator">Quantum simulator</a></li> <li><a href="/wiki/Quantum_teleportation" title="Quantum teleportation">Quantum teleportation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Extensions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantum_fluctuation" title="Quantum fluctuation">Quantum fluctuation</a></li> <li><a href="/wiki/Casimir_effect" title="Casimir effect">Casimir effect</a></li> <li><a href="/wiki/Quantum_statistical_mechanics" title="Quantum statistical mechanics">Quantum statistical mechanics</a></li> <li><a href="/wiki/Quantum_field_theory" title="Quantum field theory">Quantum field theory</a> <ul><li><a href="/wiki/History_of_quantum_field_theory" title="History of quantum field theory">History</a></li></ul></li> <li><a href="/wiki/Quantum_gravity" title="Quantum gravity">Quantum gravity</a></li> <li><a href="/wiki/Relativistic_quantum_mechanics" title="Relativistic quantum mechanics">Relativistic quantum mechanics</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat" title="Schrödinger's cat">Schrödinger's cat</a> <ul><li><a href="/wiki/Schr%C3%B6dinger%27s_cat_in_popular_culture" title="Schrödinger's cat in popular culture">in popular culture</a></li></ul></li> <li><a href="/wiki/Wigner%27s_friend" title="Wigner's friend">Wigner's friend</a></li> <li><a href="/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox" title="Einstein–Podolsky–Rosen paradox">EPR paradox</a></li> 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