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=== Single qubit ===
A [[Bell's theorem|collection of related theorems]], beginning with Bell's proof in 1964, show that quantum mechanics is incompatible with local hidden variables. However, as Bell pointed out, restricted sets of quantum phenomena ''can'' be imitated using local hidden-variable models. Bell provided a local hidden-variable model for quantum measurements upon a spin-1/2 particle, or in the terminology of quantum information theory, a single [[qubit]].<ref name=Bell1964>{{cite journal | last1 = Bell | first1 = J. S. | author-link = John Stewart Bell | year = 1964 | title = On the Einstein Podolsky Rosen Paradox | url = https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf | journal = [[Physics Physique Физика]] | volume = 1 | issue = 3| pages = 195–200 | doi = 10.1103/PhysicsPhysiqueFizika.1.195 }}</ref> Bell's model was later simplified by [[N. David Mermin]], and a closely related model was presented by [[Simon B. Kochen]] and [[Ernst Specker]].<ref>{{cite journal|first1=S. |last1=Kochen |author-link1=Simon B. Kochen |first2=E. |last2=Specker |author-link2=Ernst Specker |journal=Journal of Mathematics and Mechanics |volume=17 |year=1967 |title=The Problem of Hidden Variables in Quantum Mechanics |number=1 |pages=59–87 |jstor=24902153}}</ref><ref name="mermin1993">{{Cite journal|last=Mermin|first=N. David|author-link=David Mermin|date=1993-07-01|title=Hidden variables and the two theorems of John Bell|journal=[[Reviews of Modern Physics]]|volume=65|issue=3|pages=803–815|doi=10.1103/RevModPhys.65.803|bibcode=1993RvMP...65..803M|arxiv=1802.10119|s2cid=119546199}}</ref><ref>{{Cite journal |last1=Harrigan |first1=Nicholas |last2=Spekkens |first2=Robert W. |date=2010-02-01 |title=Einstein, Incompleteness, and the Epistemic View of Quantum States |url=https://doi.org/10.1007/s10701-009-9347-0 |journal=Foundations of Physics |language=en |volume=40 |issue=2 |pages=125–157 |arxiv=0706.2661 |doi=10.1007/s10701-009-9347-0 |s2cid=32755624 |issn=1572-9516}}</ref> The existence of these models is related to the fact that [[Gleason's theorem]] does not apply to the case of a single qubit.<ref>{{Cite journal |last1=Budroni |first1=Costantino |last2=Cabello |first2=Adán |last3=Gühne |first3=Otfried |last4=Kleinmann |first4=Matthias |last5=Larsson |first5=Jan-Åke |date=2022-12-19 |title=Kochen-Specker contextuality |url=https://link.aps.org/doi/10.1103/RevModPhys.94.045007 |journal=Reviews of Modern Physics |language=en |volume=94 |issue=4 |page=045007 |doi=10.1103/RevModPhys.94.045007 |hdl=11441/144776 |s2cid=251951089 |issn=0034-6861|hdl-access=free }}</ref>
=== Bipartite quantum states ===
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