Editing Quantum entanglement (section)

{{Short description|Physics phenomenon}}
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[[File:SPDC figure.png|thumb|[[Spontaneous parametric down-conversion]] process can split photons into type II photon pairs with mutually perpendicular polarization.]]
{{Quantum mechanics|fundamentals}}

'''Quantum entanglement''' is the phenomenon where the [[quantum state]] of each [[Subatomic particle|particle]] in a group cannot be described independently of the state of the others, even when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between [[classical physics]] and [[quantum physics]]: entanglement is a primary feature of quantum mechanics not present in classical mechanics.<ref name="horodecki2007"/>{{rp|867|q=In this way entanglement is that feature of quantum formalism which makes it impossible to simulate quantum correlations within any classical formalism.}}

[[Measurement#Quantum mechanics|Measurements]] of [[physical properties]] such as [[position (vector)|position]], [[momentum]], [[Spin (physics)|spin]], and [[polarization (waves)|polarization]] performed on entangled particles can, in some cases, be found to be perfectly [[correlated]]. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise to seemingly [[paradox]]ical effects: any measurement of a particle's properties results in an apparent and irreversible [[wave function collapse]] of that particle and changes the original quantum state. With entangled particles, such measurements affect the entangled system as a whole.

Such phenomena were the subject of a 1935 paper by [[Albert Einstein]], [[Boris Podolsky]], and [[Nathan Rosen]],<ref name="Einstein1935">
{{cite journal
 | last1      = Einstein | first1     = Albert | author-link1 = Albert Einstein
 | last2      = Podolsky | first2     = Boris  | author-link2 = Boris Podolsky
 | last3      = Rosen    | first3     = Nathan | author-link3 = Nathan Rosen
 | year=1935
 | title=Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
 | journal=Phys. Rev.
 | volume=47
 | issue=10
 | pages=777–780
 | bibcode=1935PhRv...47..777E
 | doi=10.1103/PhysRev.47.777
 | doi-access=free
}}</ref> and several papers by [[Erwin Schrödinger]] shortly thereafter,<ref name="Schrödinger1935">
{{cite journal |author=Schrödinger |first=Erwin |authorlink=Erwin Schrödinger |year=1935 |title=Discussion of probability relations between separated systems |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=31 |issue=4 |pages=555–563 |bibcode=1935PCPS...31..555S |doi=10.1017/S0305004100013554 |s2cid=121278681}}</ref><ref name="Schrödinger1936">
{{cite journal |author=Schrödinger |first=Erwin |authorlink=Erwin Schrödinger |year=1936 |title=Probability relations between separated systems |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=32 |issue=3 |pages=446–452 |bibcode=1936PCPS...32..446S |doi=10.1017/S0305004100019137 |s2cid=122822435}}
</ref> describing what came to be known as the [[EPR paradox]]. Einstein and others considered such behavior impossible, as it violated the [[local realism]] view of [[causality]] (Einstein referring to it as "spooky [[action at a distance]]")<ref>Physicist John Bell depicts the Einstein camp in this debate in his article entitled "Bertlmann's socks and the nature of reality", p. 143 of ''Speakable and unspeakable in quantum mechanics'': "For EPR that would be an unthinkable 'spooky action at a distance'. To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations. Since these real properties, fixed in advance of observation, are not contained in quantum formalism, that formalism for EPR is incomplete. It may be correct, as far as it goes, but the usual quantum formalism cannot be the whole story." And again on p. 144 Bell says: "Einstein had no difficulty accepting that affairs in different places could be correlated. What he could not accept was that an intervention at one place could influence, immediately, affairs at the other." Downloaded 5 July 2011 from {{cite book |year=1987 |access-date=14 June 2014 |title=Speakable and Unspeakable in Quantum Mechanics |first=J. S. |last=Bell |publisher=[[CERN]] |isbn=0521334950 |url=http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |url-status=dead |archive-url=https://web.archive.org/web/20150412044550/http://philosophyfaculty.ucsd.edu/faculty/wuthrich/GSSPP09/Files/BellJohnS1981Speakable_BertlmannsSocks.pdf |archive-date=12 April 2015  }}</ref> and argued that the accepted formulation of [[quantum mechanics]] must therefore be incomplete.

Later, however, the counterintuitive predictions of quantum mechanics were verified in tests where polarization or spin of entangled particles were measured at separate locations, statistically violating [[Bell's theorem|Bell's inequality]].<ref name="Clauser"/><ref name=":0" /><ref name=":1" /><ref name=":2" /> This established that the correlations produced from quantum entanglement cannot be explained in terms of [[local hidden variable theory|local hidden variables]], i.e., properties contained within the individual particles themselves.
However, despite the fact that entanglement can produce statistical [[correlation]]s between events in widely separated places, it cannot be used for [[faster-than-light communication]].<ref>{{cite book |last=Penrose |first=Roger |title=The road to reality: a complete guide to the laws of the universe |publisher=Jonathan Cape |year=2004 |isbn=978-0-224-04447-9 |location=London |page=603 |authorlink=Roger Penrose}}</ref><ref>{{cite web |last=Siegel |first=Ethan |title=No, We Still Can't Use Quantum Entanglement To Communicate Faster Than Light |url=https://www.forbes.com/sites/startswithabang/2020/01/02/no-we-still-cant-use-quantum-entanglement-to-communicate-faster-than-light/ |access-date=6 January 2023 |website=Starts with a Bang |publisher=Forbes |language=en}}</ref><ref name="Griffiths"/>{{rp|453}}
 
Quantum entanglement has been demonstrated experimentally with [[photon]]s,<ref name="Kocher1">{{cite journal |last1=Kocher |first1=C. A. |last2=Commins |first2=E. D. |year=1967 |title=Polarization Correlation of Photons Emitted in an Atomic Cascade |url=http://www.escholarship.org/uc/item/1kb7660q |journal=Physical Review Letters |volume=18 |issue=15 |pages=575–577 |bibcode=1967PhRvL..18..575K |doi=10.1103/PhysRevLett.18.575}}</ref><ref name="Kocherphd">{{cite thesis |last=Kocher |first=Carl Alvin |date=1 May 1967 |title=Polarization Correlation of Photons Emitted in an Atomic Cascade |url=https://escholarship.org/uc/item/1kb7660q |degree=PhD|publisher=University of California |language=en}}</ref> [[electron]]s,<ref name="NTR-20151021">{{cite journal |author=Hensen, B. |title=Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres |date=21 October 2015 |journal=[[Nature (journal)|Nature]] |doi=10.1038/nature15759 |display-authors=etal |volume=526 |issue=7575 |pages=682–686 |bibcode=2015Natur.526..682H |pmid=26503041 |arxiv=1508.05949 |hdl=2117/79298 |s2cid=205246446}} See also [http://www.nature.com/articles/nature15759.epdf?referrer_access_token=1QB20mTNTZW60nEXil0D79RgN0jAjWel9jnR3ZoTv0Pfu6MWINxm4Io03p2jIRZ8qX_3I3N0Kr-AlItuikCZOJrG8QbdRRghlecFwmixlbQpWuw1dtaib4Le5DQOG3u_aXHU85x1JEhOcQTa1sHi0yvW23bblxmEQZAmHL4G0gIVusG_6JWorroY5BprgbTl4FiaE8WltEgMoUMZfZBkEfbMcFDp5iR112TFx_x3ZRj88Wa23E2moEvTfKjtlued0&tracking_referrer=www.nytimes.com free online access version].</ref><ref name="NYT-20151021">{{cite news |last=Markoff |first=Jack |title=Sorry, Einstein. Quantum Study Suggests 'Spooky Action' Is Real. |url=https://www.nytimes.com/2015/10/22/science/quantum-theory-experiment-said-to-prove-spooky-interactions.html |date=21 October 2015 |work=The New York Times |access-date=21 October 2015 }}</ref> [[top quark]]s,<ref>{{cite web | url=https://physicsworld.com/a/quantum-entanglement-observed-in-top-quarks/ | title=Quantum entanglement observed in top quarks | date=11 October 2023 |website=[[Physics World]] |first=Martijn |last=Boerkamp}}</ref> molecules<ref>{{cite journal |last1=Holland |first1=Connor M. |last2=Lu |first2=Yukai |last3=Cheuk |first3=Lawrence W. |date=8 December 2023 |title=On-demand entanglement of molecules in a reconfigurable optical tweezer array |url=https://www.science.org/doi/10.1126/science.adf4272 |journal=Science |language=en |volume=382 |issue=6675 |pages=1143–1147 |doi=10.1126/science.adf4272 |pmid=38060644 |issn=0036-8075|arxiv=2210.06309 |bibcode=2023Sci...382.1143H }}</ref> and even small diamonds.<ref>{{cite journal |journal=Science |date=2 December 2011 |volume=334 |issue=6060 |pages=1253–1256 |doi=10.1126/science.1211914 |pmid=22144620 |title=Entangling macroscopic diamonds at room temperature |bibcode = 2011Sci...334.1253L |last1=Lee |first1=K. C. |last2=Sprague |first2=M. R. |last3=Sussman |first3=B. J. |last4=Nunn |first4=J. |last5=Langford |first5=N. K. |last6=Jin |first6=X.-M. |last7=Champion |first7=T. |last8=Michelberger |first8=P. |last9=Reim |first9=K. F. |last10=England |first10=D. |last11=Jaksch |first11=D. |last12=Walmsley |first12=I. A. |s2cid=206536690 |display-authors=4}}</ref> The use of quantum entanglement in [[quantum communication|communication]] and [[quantum computing|computation]] is an active area of research and development.