Non-Contextual and Local Hidden-Variable Model for the Peres-Mermin and Greenberger-Horne-Zeilinger Systems

TL;DR

This paper proposes a hidden-variable model for quantum spin systems that is compatible with non-contextuality and locality assumptions, challenging traditional no-hidden-variables arguments by replacing scalar spin values with orientation vectors.

Contribution

It introduces a novel hidden-variable model for spin systems that aligns with both non-contextuality and locality, offering a new perspective on foundational quantum arguments.

Findings

Model reproduces quantum spin correlations

Compatible with Peres-Mermin and GHZ systems

Challenges traditional no-hidden-variables conclusions

Abstract

A hidden-variable model for quantum-mechanical spin, as represented by the Pauli spin operators, is proposed for systems illustrating the well-known no-hidden-variables arguments by Peres and Mermin (1990) and by Greenberger, Horne, and Zeilinger (1989). Both arguments rely on an assumption of non-contextuality; the latter argument can also be phrased as a non-locality argument, using a locality assumption. The model suggested here is compatible with both assumptions. This is possible because the scalar values of spin observables are replaced by vectors that are components of orientations.