Editing Quantum entanglement (section)

== Nonlocality and entanglement ==
As discussed above, entanglement is necessary to produce a violation of a [[Bell's theorem|Bell inequality]]. However, the mere presence of entanglement alone is insufficient,<ref name="Brunner-RMP2014">
{{cite journal
 | title=Bell nonlocality
 | last1 = Brunner | first1 = Nicolas
 | last2 = Cavalcanti | first2 = Daniel
 | last3 = Pironio | first3 = Stefano
 | last4 = Scarani | first4 = Valerio
 | last5 = Wehner | first5 = Stephanie
 | journal= Reviews of Modern Physics
 | volume=86
 | issue=2
 | pages=419–478
 | date=2014
 | doi=10.1103/RevModPhys.86.419
 | arxiv=1303.2849
 | bibcode=2014RvMP...86..419B
 | s2cid=119194006
}}</ref> as Bell himself noted in his 1964 paper.<ref name=":4" /> This is demonstrated, for example, by [[Werner state]]s, which are a family of states describing pairs of particles. For appropriate choices of the key parameter that identifies a given Werner state within the full set thereof, the Werner states exhibit entanglement. Yet pairs of particles described by Werner states always admit a local hidden variable model. In other words, these states cannot power the violation of a Bell inequality, despite possessing entanglement.<ref name="werner1989">{{cite journal |last=Werner |first=R. F. |author-link=Reinhard F. Werner |year=1989 |title=Quantum States with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model |journal=[[Physical Review A]] |volume=40 |issue=8 |pages=4277–4281 |bibcode=1989PhRvA..40.4277W |doi=10.1103/PhysRevA.40.4277 |pmid=9902666}}</ref> This can be generalized from pairs of particles to larger collections as well.<ref name="Augusiak2015">
{{cite journal
 | last1 = Augusiak | first1 = R.
 | last2 = Demianowicz | first2 = M.
 | last3 = Tura | first3 = J.
 | last4 = Acín | first4 = A.
 | title = Entanglement and nonlocality are inequivalent for any number of parties
 | journal = Physical Review Letters
 | volume = 115
 | issue = 3
 | pages = 030404
 | year = 2015
 | arxiv = 1407.3114
 | doi = 10.1103/PhysRevLett.115.030404
 | pmid = 26230773
 | hdl = 2117/78836
 | bibcode = 2015PhRvL.115c0404A
 | s2cid = 29758483
}}</ref>

The violation of Bell inequalities is often called ''[[quantum nonlocality]].'' This term is not without controversy.<ref>{{cite SEP|title=Action at a Distance in Quantum Mechanics |url-id=qm-action-distance |author-first=Joseph |author-last=Berkovitz |date=2007-01-26}}</ref> It is sometimes argued that using the term ''nonlocality'' carries the unwarranted implication that the violation of Bell inequalities must be explained by physical, faster-than-light signals.<ref name="Scarani">{{cite book|first=Valerio |last=Scarani |title=Bell Nonlocality |publisher=Oxford University Press |year=2019 |isbn=978-0-19-878841-6 |page=8}}</ref> In other words, the failure of local hidden-variable models to reproduce quantum mechanics is not necessarily a sign of true nonlocality in quantum mechanics itself.<ref>{{cite book|first=Roland |last=Omnès |author-link=Roland Omnès |title=The Interpretation of Quantum Mechanics |publisher=Princeton University Press |year=1994 |isbn=978-0-691-03669-4 |pages=399–400}}</ref><ref>{{cite journal|last=Mermin |first=N. D. |author-link=N. David Mermin |title=What Do These Correlations Know About Reality? Nonlocality and the Absurd |journal=[[Foundations of Physics]] |volume=29 |year=1999 |issue=4 |pages=571–587 |arxiv=quant-ph/9807055 |bibcode=1998quant.ph..7055M |doi=10.1023/A:1018864225930}}</ref><ref>{{cite book|last=Żukowski |first=Marek |title=Quantum &#91;Un&#93;Speakables II |chapter=Bell's Theorem Tells Us Not What Quantum Mechanics is, but What Quantum Mechanics is Not |date=2017 |series=The Frontiers Collection |pages=175–185 |editor-last=Bertlmann |editor-first=Reinhold |place=Cham |publisher=Springer International Publishing |doi=10.1007/978-3-319-38987-5_10 |isbn=978-3-319-38985-1 |editor2-last=Zeilinger |editor2-first=Anton |editor-link2=Anton Zeilinger |arxiv=1501.05640}}</ref> Despite these reservations, the term ''nonlocality'' has become a widespread convention.<ref name="Scarani"/>

The term ''nonlocality'' is also sometimes applied to other concepts besides the nonexistence of a local hidden-variable model, such as [[unextendible product basis|whether states can be distinguished by local measurements]].<ref>{{cite journal |last1=Bennett |first1=Charles H. |last2=DiVincenzo |first2=David P. |last3=Fuchs |first3=Christopher A. |last4=Mor |first4=Tal |last5=Rains |first5=Eric |last6=Shor |first6=Peter W. |last7=Smolin |first7=John A. |last8=Wootters |first8=William K. |year=1999 |title=Quantum nonlocality without entanglement |journal=Physical Review A |volume=59 |issue=2 |pages=1070–1091 |arxiv=quant-ph/9804053 |bibcode=1999PhRvA..59.1070B |doi=10.1103/PhysRevA.59.1070 |s2cid=15282650}}</ref> Moreover, [[quantum field theory]] is often said to be ''local'' because [[observable]]s defined within spacetime regions that are [[spacelike]] separated must commute.<ref name="Brunner-RMP2014"/><ref>{{cite book|last=Haag |first=Rudolf |author-link=Rudolf Haag |title=Local Quantum Physics: Fields, Particles, Algebras |edition=2nd |publisher=Springer |pages=107–108 |isbn=3-540-61451-6 |year=1996}}</ref> These other uses of ''local'' and ''nonlocal'' are not discussed further here.