Editing Bell's theorem (section)

===Quasiclassical entanglement===
{{main|Spekkens toy model|Werner state}}
As Bell pointed out, some predictions of quantum mechanics can be replicated in local hidden-variable models, including special cases of correlations produced from entanglement. This topic has been studied systematically in the years since Bell's theorem. In 1989, [[Reinhard F. Werner|Reinhard Werner]] introduced what are now called [[Werner state]]s, joint quantum states for a pair of systems that yield EPR-type correlations but also admit a hidden-variable model.<ref>{{Cite journal |last=Werner |first=Reinhard F. |author-link=Reinhard F. Werner |date=1989-10-01 |title=Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model |journal=[[Physical Review A]] |language=en |volume=40 |issue=8 |pages=4277–4281 |bibcode=1989PhRvA..40.4277W |doi=10.1103/PhysRevA.40.4277 |pmid=9902666 |issn=0556-2791}}</ref> Werner states are bipartite quantum states that are invariant under [[Unitarity (physics)|unitaries]] of symmetric [[Kronecker product|tensor-product]] form: <math display="block">\rho_{AB} = (U \otimes U) \rho_{AB} (U^\dagger \otimes U^\dagger).</math>
In 2004, [[Robert Spekkens]] introduced a [[Spekkens toy model|toy model]] that starts with the premise of local, discretized degrees of freedom and then imposes a "knowledge balance principle" that restricts how much an observer can know about those degrees of freedom, thereby making them into hidden variables. The allowed states of knowledge ("epistemic states") about the underlying variables ("ontic states") mimic some features of quantum states. Correlations in the toy model can emulate some aspects of entanglement, like [[monogamy of entanglement|monogamy]], but by construction, the toy model can never violate a Bell inequality.<ref>{{Cite journal |author1-link=Robert Spekkens |last=Spekkens |first=Robert W. |date=2007-03-19 |title=Evidence for the epistemic view of quantum states: A toy theory |journal=[[Physical Review A]] |language=en |volume=75 |issue=3 |pages=032110 |arxiv=quant-ph/0401052 |bibcode=2007PhRvA..75c2110S |doi=10.1103/PhysRevA.75.032110 |s2cid=117284016 |issn=1050-2947}}</ref><ref>{{Cite journal |last1=Catani |first1=Lorenzo |last2=Browne |first2=Dan E. |date=2017-07-27 |title=Spekkens' toy model in all dimensions and its relationship with stabiliser quantum mechanics |journal=[[New Journal of Physics]] |volume=19 |issue=7 |pages=073035 |doi=10.1088/1367-2630/aa781c |bibcode=2017NJPh...19g3035C |s2cid=119428107 |issn=1367-2630 |doi-access=free |arxiv=1701.07801 }}</ref>