Local hidden-variable theory
The mathematical implications of a local hidden-variable theory with regards to quantum entanglement were explored by physicist John Stewart Bell, who in 1964 proved that broad classes of local hidden-variable theories cannot reproduce the correlations between measurement outcomes that quantum mechanics predicts, a result since confirmed by a range of detailed Bell test experiments.[1] A 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.[3][4][5] The existence of these models is related to the fact that Gleason's theorem does not apply to the case of a single qubit.[2][7][8] For separable states of two particles, there is a simple hidden-variable model for any measurements on the two parties.Surprisingly, there are also entangled states for which all von Neumann measurements can be described by a hidden-variable model.Reinhard F. Werner showed that such states allow for a hidden-variable model forA hidden-variable model for any von Neumann measurements at the parties has been presented for a three-qubit quantum state.[13] Previously some new hypotheses were conjectured concerning the role of time in constructing hidden-variables theory.One approach was suggested by K. Hess and W. Philipp and relies upon possible consequences of time dependencies of hidden variables; this hypothesis has been criticized by Richard D. Gill, Gregor Weihs [de], Anton Zeilinger and Marek Żukowski, as well as D. M.