Physics:Quantum nonlocality - Revision history

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	{{Quantum book backlink\|Conceptual and interpretations}}		{{Quantum book backlink\|Conceptual and interpretations}}
	{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}		{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}
	~~{{Quantum mechanics\|cTopic=Fundamental concepts}}~~
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	* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}		* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}
	* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}		* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}
	~~[[Category:Quantum measurement\|Nonlocality]]~~
	~~[[Category:Quantum field theory\|Nonlocality]]~~

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum nonlocality\|1}}		{{Sourceattribution\|Physics:Quantum nonlocality\|1}}

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	* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}		* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}
	* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}		* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}

	~~{{Quantum mechanics topics}}~~

	[[Category:Quantum measurement\|Nonlocality]]		[[Category:Quantum measurement\|Nonlocality]]
	[[Category:Quantum field theory\|Nonlocality]]		[[Category:Quantum field theory\|Nonlocality]]

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	===Dimension witnesses===		===Dimension witnesses===
	The degree of non-locality of a quantum box <math>P(a,b\|x,y)</math> can also provide lower bounds on the Hilbert space dimension of the local systems accessible to Alice and Bob.<ref name="WITNESS">{{cite journal\|first=Nicolas\|last= Brunner\|author2= Pironio, Stefano\|author3= Acín, Antonio\|author4= Gisin, Nicolas\|author5= Methot, Andre Allan\|author6= Scarani, Valerio\|title= Testing the Hilbert space dimension\|journal= Physical Review Letters\|volume= 100\|issue= 21\|article-number= 210503\|year=2008\|doi= 10.1103/PhysRevLett.100.210503\|pmid= 18518591\|arxiv= 0802.0760\|bibcode= 2008arXiv0802.0760B\|s2cid= 119256543}}</ref> This problem is equivalent to deciding the existence of a matrix with low completely positive semidefinite rank.<ref name="CONES2">{{cite journal\|first=Anupam\|last= Prakash\|author2= Sikora, Jamie\| author3=Varvitsiotis, Antonios\|author4= Wei Zhaohui\|title= Completely positive semidefinite rank\|journal=Mathematical Programming\| volume= 171\| issue= 1–2\|pages= 397–431\|year=2018\|doi= 10.1007/s10107-017-1198-4\|arxiv= 1604.07199\|s2cid= 17885968}}</ref> Finding lower bounds on the Hilbert space dimension based on statistics happens to be a hard task, and current general methods only provide very low estimates.<ref name="FINITE">{{cite journal\|first=Miguel\|last= Navascués\| author2= Vértesi, Tamás\|title= Bounding the set of finite dimensional quantum correlations\|journal= Physical Review Letters\|volume= 115\|issue= 2\|article-number= 020501\|year= 2015\|doi=10.1103/PhysRevLett.115.020501\|pmid= 26207454\|bibcode= 2015PhRvL.115b0501N\|arxiv= 1412.0924\|s2cid= 12226163}}</ref> However, a Bell scenario with five inputs and three outputs suffices to provide arbitrarily high lower bounds on the underlying Hilbert space dimension.<ref name="COLA">{{ cite arXiv\|first=Andrea\|last=Coladangelo\|author2= Stark, Jalex\|title= Unconditional separation of finite and infinite-dimensional quantum correlations\| eprint=1804.05116\|class=quant-ph\|year=2018}}</ref> Quantum communication protocols which assume a knowledge of the local dimension of Alice and Bob's systems, but otherwise do not make claims on the mathematical description of the preparation and measuring devices involved are termed semi-device independent protocols. Currently, there exist semi-device independent protocols for quantum key distribution <ref name="SEMIQKD">{{cite journal\|first=Marcin\|last= Pawlowski \|author2= Brunner, Nicolas\| title=Semi-device-independent security of one-way quantum key distribution\|journal= Physical Review A\|volume=84\|issue= 1 \|pages= 010302(R)\|year= 2011\|doi= 10.1103/PhysRevA.84.010302 \|bibcode= 2011PhRvA..84a0302P \|arxiv= 1103.4105 \|s2cid= 119300029 }}</ref> and randomness expansion.<ref name = "SEMIEXP">{{cite journal\|first=Hong-Wei\|last= Li\|author2= Yin, Zhen-Qiang\|author3= Wu, Yu-Chun\|author4= Zou, Xu-Bo \|author5= Wang, Shuang\|author6= Chen, Wei\|author7= Guo, Guang-Can\| author8= Han, Zheng-Fu\|title= Semi-device-independent random-number expansion without entanglement\|journal= Physical Review A\|volume= 84\|issue= 3\|article-number= 034301\|year= 2011\|doi= 10.1103/PhysRevA.84.034301\|bibcode= 2011PhRvA..84c4301L\|arxiv= 1108.1480\|s2cid= 118407749}}</ref>		The degree of non-locality of a quantum box <math>P(a,b\|x,y)</math> can also provide lower bounds on the Hilbert space dimension of the local systems accessible to Alice and Bob.<ref name="WITNESS">{{cite journal\|first=Nicolas\|last= Brunner\|author2= Pironio, Stefano\|author3= Acín, Antonio\|author4= Gisin, Nicolas\|author5= Methot, Andre Allan\|author6= Scarani, Valerio\|title= Testing the Hilbert space dimension\|journal= Physical Review Letters\|volume= 100\|issue= 21\|article-number= 210503\|year=2008\|doi= 10.1103/PhysRevLett.100.210503\|pmid= 18518591\|arxiv= 0802.0760\|bibcode= 2008arXiv0802.0760B\|s2cid= 119256543}}</ref> This problem is equivalent to deciding the existence of a matrix with low completely positive semidefinite rank.<ref name="CONES2">{{cite journal\|first=Anupam\|last= Prakash\|author2= Sikora, Jamie\| author3=Varvitsiotis, Antonios\|author4= Wei Zhaohui\|title= Completely positive semidefinite rank\|journal=Mathematical Programming\| volume= 171\| issue= 1–2\|pages= 397–431\|year=2018\|doi= 10.1007/s10107-017-1198-4\|arxiv= 1604.07199\|s2cid= 17885968}}</ref> Finding lower bounds on the Hilbert space dimension based on statistics happens to be a hard task, and current general methods only provide very low estimates.<ref name="FINITE">{{cite journal\|first=Miguel\|last= Navascués\| author2= Vértesi, Tamás\|title= Bounding the set of finite dimensional quantum correlations\|journal= Physical Review Letters\|volume= 115\|issue= 2\|article-number= 020501\|year= 2015\|doi=10.1103/PhysRevLett.115.020501\|pmid= 26207454\|bibcode= 2015PhRvL.115b0501N\|arxiv= 1412.0924\|s2cid= 12226163}}</ref> However, a Bell scenario with five inputs and three outputs suffices to provide arbitrarily high lower bounds on the underlying Hilbert space dimension.<ref name="COLA">{{ cite arXiv\|first=Andrea\|last=Coladangelo\|author2= Stark, Jalex\|title= Unconditional separation of finite and infinite-dimensional quantum correlations\| eprint=1804.05116\|class=quant-ph\|year=2018}}</ref> Quantum communication protocols which assume a knowledge of the local dimension of Alice and Bob's systems, but otherwise do not make claims on the mathematical description of the preparation and measuring devices involved are termed semi-device independent protocols. Currently, there exist semi-device independent protocols for quantum key distribution <ref name="SEMIQKD">{{cite journal\|first=Marcin\|last= Pawlowski \|author2= Brunner, Nicolas\| title=Semi-device-independent security of one-way quantum key distribution\|journal= Physical Review A\|volume=84\|issue= 1 \|pages= 010302(R)\|year= 2011\|doi= 10.1103/PhysRevA.84.010302 \|bibcode= 2011PhRvA..84a0302P \|arxiv= 1103.4105 \|s2cid= 119300029 }}</ref> and randomness expansion.<ref name = "SEMIEXP">{{cite journal\|first=Hong-Wei\|last= Li\|author2= Yin, Zhen-Qiang\|author3= Wu, Yu-Chun\|author4= Zou, Xu-Bo \|author5= Wang, Shuang\|author6= Chen, Wei\|author7= Guo, Guang-Can\| author8= Han, Zheng-Fu\|title= Semi-device-independent random-number expansion without entanglement\|journal= Physical Review A\|volume= 84\|issue= 3\|article-number= 034301\|year= 2011\|doi= 10.1103/PhysRevA.84.034301\|bibcode= 2011PhRvA..84c4301L\|arxiv= 1108.1480\|s2cid= 118407749}}</ref>

	~~==See also==~~
	*Action at a distance
	*Buscemi nonlocality
	*Popper's experiment
	*[[Physics:Quantum pseudo-telepathy\|Quantum pseudo-telepathy]]
	*[[Physics:Quantum contextuality\|Quantum contextuality]]
	*[[Physics:Quantum foundations\|Quantum foundations]]

	== See also ==		== See also ==

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	===Einstein, Podolsky and Rosen===		===Einstein, Podolsky and Rosen===
	~~{{Main\|Physics~~:EPR paradox}}		''Related topic:'' EPR paradox

	In the 1935 EPR paper,<ref name=EPR>{{Cite journal \|last1=Einstein \|first1=A. \|last2=Podolsky \|first2=B. \|last3=Rosen \|first3=N. \|date=1935-05-15 \|title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? \|journal=Physical Review \|language=en \|volume=47 \|issue=10 \|pages=777–780 \|doi=10.1103/PhysRev.47.777 \|issn=0031-899X\|doi-access=free \|bibcode=1935PhRv...47..777E }}</ref> [[Biography:Albert Einstein\|Albert Einstein]], Boris Podolsky and Nathan Rosen described "two spatially separated particles which have both perfectly correlated positions and momenta"<ref name=Colloquium >{{Cite journal \|last1=Reid \|first1=M. D. \|last2=Drummond \|first2=P. D. \|last3=Bowen \|first3=W. P. \|last4=Cavalcanti \|first4=E. G. \|last5=Lam \|first5=P. K. \|last6=Bachor \|first6=H. A. \|last7=Andersen \|first7=U. L. \|last8=Leuchs \|first8=G. \|date=2009-12-10 \|title=Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications \|url=https://link.aps.org/doi/10.1103/RevModPhys.81.1727 \|journal=Reviews of Modern Physics \|language=en \|volume=81 \|issue=4 \|pages=1727–1751 \|doi=10.1103/RevModPhys.81.1727 \|arxiv=0806.0270 \|bibcode=2009RvMP...81.1727R \|issn=0034-6861\|hdl=10072/37941 \|hdl-access=free }}</ref> as a direct consequence of quantum theory. They intended to use the classical principle of locality to challenge the idea that the quantum wavefunction was a complete description of reality, but instead they sparked a debate on the nature of reality.<ref name=ClauserShimony1978>Clauser, John F., and Abner Shimony. "[https://duneece.wiscweb.wisc.edu/wp-content/uploads/sites/605/2019/01/J_F_Clauser_1978_Rep._Prog._Phys._41_002_bell_test.pdf Bell's theorem. Experimental tests and implications.]" Reports on Progress in Physics 41.12 (1978): 1881.</ref>		In the 1935 EPR paper,<ref name=EPR>{{Cite journal \|last1=Einstein \|first1=A. \|last2=Podolsky \|first2=B. \|last3=Rosen \|first3=N. \|date=1935-05-15 \|title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? \|journal=Physical Review \|language=en \|volume=47 \|issue=10 \|pages=777–780 \|doi=10.1103/PhysRev.47.777 \|issn=0031-899X\|doi-access=free \|bibcode=1935PhRv...47..777E }}</ref> [[Biography:Albert Einstein\|Albert Einstein]], Boris Podolsky and Nathan Rosen described "two spatially separated particles which have both perfectly correlated positions and momenta"<ref name=Colloquium >{{Cite journal \|last1=Reid \|first1=M. D. \|last2=Drummond \|first2=P. D. \|last3=Bowen \|first3=W. P. \|last4=Cavalcanti \|first4=E. G. \|last5=Lam \|first5=P. K. \|last6=Bachor \|first6=H. A. \|last7=Andersen \|first7=U. L. \|last8=Leuchs \|first8=G. \|date=2009-12-10 \|title=Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications \|url=https://link.aps.org/doi/10.1103/RevModPhys.81.1727 \|journal=Reviews of Modern Physics \|language=en \|volume=81 \|issue=4 \|pages=1727–1751 \|doi=10.1103/RevModPhys.81.1727 \|arxiv=0806.0270 \|bibcode=2009RvMP...81.1727R \|issn=0034-6861\|hdl=10072/37941 \|hdl-access=free }}</ref> as a direct consequence of quantum theory. They intended to use the classical principle of locality to challenge the idea that the quantum wavefunction was a complete description of reality, but instead they sparked a debate on the nature of reality.<ref name=ClauserShimony1978>Clauser, John F., and Abner Shimony. "[https://duneece.wiscweb.wisc.edu/wp-content/uploads/sites/605/2019/01/J_F_Clauser_1978_Rep._Prog._Phys._41_002_bell_test.pdf Bell's theorem. Experimental tests and implications.]" Reports on Progress in Physics 41.12 (1978): 1881.</ref>
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	=== Bell inequality ===		=== Bell inequality ===
	~~{{See also\|~~Bell's theorem\|Bell test experiments}}		''Related topic:'' Bell's theorem, Bell test experiments

	In 1964 John Bell answered Einstein's question by showing that such local hidden variables can never reproduce the full range of statistical outcomes predicted by quantum theory.<ref name="BELL">{{cite journal \| last = Bell\| first = John \| title = On the Einstein Podolsky Rosen paradox \| journal = Physics Physique Физика \| volume = 1 \| issue = 3 \| pages = 195–200 \| year = 1964 \| doi = 10.1103/PhysicsPhysiqueFizika.1.195 \| doi-access = free \| bibcode = 1964PhyNY...1..195B }}</ref> Bell showed that a local hidden variable hypothesis leads to restrictions on the strength of correlations of measurement results. If the Bell inequalities are violated experimentally as predicted by quantum mechanics, then reality cannot be described by local hidden variables and the mystery of quantum nonlocal causation remains. However, Bell notes that the non-local hidden variable model of Bohm are different:<ref name="BELL"/>		In 1964 John Bell answered Einstein's question by showing that such local hidden variables can never reproduce the full range of statistical outcomes predicted by quantum theory.<ref name="BELL">{{cite journal \| last = Bell\| first = John \| title = On the Einstein Podolsky Rosen paradox \| journal = Physics Physique Физика \| volume = 1 \| issue = 3 \| pages = 195–200 \| year = 1964 \| doi = 10.1103/PhysicsPhysiqueFizika.1.195 \| doi-access = free \| bibcode = 1964PhyNY...1..195B }}</ref> Bell showed that a local hidden variable hypothesis leads to restrictions on the strength of correlations of measurement results. If the Bell inequalities are violated experimentally as predicted by quantum mechanics, then reality cannot be described by local hidden variables and the mystery of quantum nonlocal causation remains. However, Bell notes that the non-local hidden variable model of Bohm are different:<ref name="BELL"/>
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	==Entanglement and nonlocality==		==Entanglement and nonlocality==
	~~{{See also\|~~Quantum entanglement}}		''Related topic:'' Quantum entanglement
	Quantum nonlocality is sometimes understood as being equivalent to entanglement. However, this is not the case. Quantum entanglement can be defined only within the formalism of quantum mechanics, i.e., it is a model-dependent property. In contrast, nonlocality refers to the impossibility of a description of observed statistics in terms of a local hidden variable model, so it is independent of the physical model used to describe the experiment.		Quantum nonlocality is sometimes understood as being equivalent to entanglement. However, this is not the case. Quantum entanglement can be defined only within the formalism of quantum mechanics, i.e., it is a model-dependent property. In contrast, nonlocality refers to the impossibility of a description of observed statistics in terms of a local hidden variable model, so it is independent of the physical model used to describe the experiment.

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	===Device-independent quantum key distribution===		===Device-independent quantum key distribution===
	~~{{Main\|~~Device-independent quantum cryptography}}		''Related topic:'' Device-independent quantum cryptography
	The first device-independent protocol proposed was device-independent quantum key distribution (QKD).<ref name="YAO">{{cite conference\|last=Mayers\|first= Dominic\|author2= Yao, Andrew C.-C.\|year=1998\|title= Quantum Cryptography with Imperfect Apparatus\| conference=IEEE Symposium on Foundations of Computer Science (FOCS) }}</ref> In this primitive, two distant parties, Alice and Bob, are distributed an entangled quantum state, that they probe, thus obtaining the statistics <math>P(a,b\|x,y)</math>. Based on how non-local the box <math>P(a,b\|x,y)</math> happens to be, Alice and Bob estimate how much knowledge an external quantum adversary Eve (the eavesdropper) could possess on the value of Alice and Bob's outputs. This estimation allows them to devise a reconciliation protocol at the end of which Alice and Bob share a perfectly correlated one-time pad of which Eve has no information whatsoever. The one-time pad can then be used to transmit a secret message through a public channel. Although the first security analyses on device-independent QKD relied on Eve carrying out a specific family of attacks,<ref name="DIQKD">{{cite journal\|first=Antonio\|last= Acín\| author2=Nicolas Gisin\|author3= Lluis Masanes\|title= From Bell's Theorem to Secure Quantum Key Distribution\|journal= Physical Review Letters\|volume=97\|issue= 12\|article-number= 120405\|year=2006\|doi=10.1103/PhysRevLett.97.120405\|pmid= 17025944\|bibcode= 2006PhRvL..97l0405A\|arxiv= quant-ph/0510094\|s2cid= 3315286}}</ref> all such protocols have been recently proven unconditionally secure.<ref name="VAZIRANI">{{cite journal\|last=Vazirani\|first= Umesh\|author2= Vidick, Thomas\|year=2014\|title=Fully Device-Independent Quantum Key Distribution\|journal= Physical Review Letters\|volume= 113\|issue=14\|article-number= 140501\|doi= 10.1103/physrevlett.113.140501\|pmid= 25325625\|bibcode= 2014PhRvL.113n0501V\|arxiv= 1210.1810\|s2cid= 119299119}}</ref>		The first device-independent protocol proposed was device-independent quantum key distribution (QKD).<ref name="YAO">{{cite conference\|last=Mayers\|first= Dominic\|author2= Yao, Andrew C.-C.\|year=1998\|title= Quantum Cryptography with Imperfect Apparatus\| conference=IEEE Symposium on Foundations of Computer Science (FOCS) }}</ref> In this primitive, two distant parties, Alice and Bob, are distributed an entangled quantum state, that they probe, thus obtaining the statistics <math>P(a,b\|x,y)</math>. Based on how non-local the box <math>P(a,b\|x,y)</math> happens to be, Alice and Bob estimate how much knowledge an external quantum adversary Eve (the eavesdropper) could possess on the value of Alice and Bob's outputs. This estimation allows them to devise a reconciliation protocol at the end of which Alice and Bob share a perfectly correlated one-time pad of which Eve has no information whatsoever. The one-time pad can then be used to transmit a secret message through a public channel. Although the first security analyses on device-independent QKD relied on Eve carrying out a specific family of attacks,<ref name="DIQKD">{{cite journal\|first=Antonio\|last= Acín\| author2=Nicolas Gisin\|author3= Lluis Masanes\|title= From Bell's Theorem to Secure Quantum Key Distribution\|journal= Physical Review Letters\|volume=97\|issue= 12\|article-number= 120405\|year=2006\|doi=10.1103/PhysRevLett.97.120405\|pmid= 17025944\|bibcode= 2006PhRvL..97l0405A\|arxiv= quant-ph/0510094\|s2cid= 3315286}}</ref> all such protocols have been recently proven unconditionally secure.<ref name="VAZIRANI">{{cite journal\|last=Vazirani\|first= Umesh\|author2= Vidick, Thomas\|year=2014\|title=Fully Device-Independent Quantum Key Distribution\|journal= Physical Review Letters\|volume= 113\|issue=14\|article-number= 140501\|doi= 10.1103/physrevlett.113.140501\|pmid= 25325625\|bibcode= 2014PhRvL.113n0501V\|arxiv= 1210.1810\|s2cid= 119299119}}</ref>

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	*[[Physics:Quantum contextuality\|Quantum contextuality]]		*[[Physics:Quantum contextuality\|Quantum contextuality]]
	*[[Physics:Quantum foundations\|Quantum foundations]]		*[[Physics:Quantum foundations\|Quantum foundations]]

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	==References==		==References==
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	[[Category:Quantum field theory\|Nonlocality]]		[[Category:Quantum field theory\|Nonlocality]]

	{{Sourceattribution\|Quantum nonlocality}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum nonlocality\|1}}

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	~~{{Quantum mechanics\|cTopic=Fundamental concepts}}~~
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	* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}		* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}
	* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}		* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}
	~~[[Category:Quantum measurement\|Nonlocality]]~~
	~~[[Category:Quantum field theory\|Nonlocality]]~~

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum nonlocality\|1}}		{{Sourceattribution\|Physics:Quantum nonlocality\|1}}

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	* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}		* {{cite book \|author=Cramer, JG \|title=The Quantum Handshake: Entanglement, Nonlocality and Transactions \|publisher=Springer Verlag \|year=2015 \|isbn=978-3-319-24642-0 }}
	* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}		* {{cite book \|author=Duarte, FJ \|title=Fundamentals of Quantum Entanglement \|publisher=Institute of Physics (UK) \|year=2019 \|isbn=978-0-7503-2226-3 }}

	~~{{Quantum mechanics topics}}~~

	[[Category:Quantum measurement\|Nonlocality]]		[[Category:Quantum measurement\|Nonlocality]]
	[[Category:Quantum field theory\|Nonlocality]]		[[Category:Quantum field theory\|Nonlocality]]

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	{{Quantum book backlink\|Conceptual and interpretations}}		{{Quantum book backlink\|Conceptual and interpretations}}
	{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}		{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}
	{{Quantum mechanics\|cTopic=Fundamental concepts}}		{{Quantum mechanics\|cTopic=Fundamental concepts}}

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← Older revision		Revision as of 11:09, 22 May 2026
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	{{short description\|Deviations from local realism}}		{{short description\|Deviations from local realism}}

	{{Quantum book backlink\|Conceptual and interpretations}}		{{Quantum book backlink\|Conceptual and interpretations}}
	{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}		{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}

← Older revision		Revision as of 12:23, 20 May 2026
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	{{short description\|Deviations from local realism}}		{{short description\|Deviations from local realism}}

	{{Quantum book backlink\|Conceptual and interpretations}}		{{Quantum book backlink\|Conceptual and interpretations}}
			{{Quantum article nav\|previous=Physics:Quantum Hidden variable theory\|previous label=Hidden variable theory\|next=Physics:Quantum contextuality\|next label=Contextuality}}
	{{Quantum mechanics\|cTopic=Fundamental concepts}}		{{Quantum mechanics\|cTopic=Fundamental concepts}}