Hidden variable models for quantum mechanics can have local parts

TL;DR

This paper challenges a claim that hidden variable models for quantum mechanics must be trivial in their local parts, showing that nonlocal models can indeed have nontrivial local components if certain restrictions are relaxed.

Contribution

The authors identify a restriction in previous work that limits the division of hidden variable models into local and nonlocal parts, and provide an explicit model demonstrating nontrivial local hidden variables.

Findings

CR's restriction implies local parts are trivial

Explicit nonlocal model with nontrivial local variables

Restriction on nonlocal part is not physically motivated

Abstract

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.