Hidden-variable models for quantum mechanics

Robert A. Van Wesep

Simon Kochen, Ernst P. Specker

Atul Singh Arora, Arvind Arvind

We propose a non-contextual hidden variable model, consistent with all predictions of quantum mechanics (QM). A careful scrutiny of consistency requirements of any hidden variable model with quantum mechanics and the corresponding no-go theorems, leads us to the conclusion that the notion of contextuality is not a necessary feature of QM. The alternative view that emerges, hinges on identifying a new classical property which we call multiplicativity. It turns out that by relaxing this condition of multiplicativity on hidden variable models, they can be made consistent with QM. The connection of non-multiplicativity to Bohm's model and to apparent contextuality is also discussed.

Simon Kochen, Ernst P. Specker

Roger Colbeck, Renato Renner

It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely nonlocal, then any quantum mechanical predictions can be recovered. In this Letter, we consider general hidden variable models which can have both local and nonlocal parts. We show the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a nontrivial local part, such as the model proposed by Leggett.

Jan-Åke Larsson, Adán Cabello

We criticize Colbeck and Renner's (CR's) statement that "any hidden variable model can only be compatible with quantum mechanics if its local part is trivial" [Phys. Rev. Lett. 101, 050403 (2008)]. We note that CR's attempt to divide a nonlocal hidden variable model into a "local part" and a "nonlocal part" contains a restriction on the latter. This restriction implies that the division is really into a "local part" and a "nonsignaling nonlocal part." CR's nonsignaling requirement on the "nonlocal part" cannot be physically motivated, since the hidden variables cannot be accessed by experimenters. Nor is it a natural mathematical generalization from the local hidden variable case, since it is simple to make a generalization without CR's requirement. We give an explicit nonlocal hidden variable model that, in the case the restriction is not enforced, contains nontrivial local hidden variables.