Three noncontextual hidden variable models for the Peres-Mermin square

TL;DR

This paper challenges the common interpretation of the Peres-Mermin square by constructing three hidden variable models that violate certain physical realization assumptions, suggesting noncontextual models may still be viable.

Contribution

It introduces three explicit hidden variable models for the Peres-Mermin square that violate standard physical realization assumptions, questioning the interpretation of contextuality.

Findings

Models demonstrate noncontextual hidden variables can exist under relaxed assumptions

Violations of physical realization conditions undermine the Peres-Mermin square's implications

Supports alternative interpretations of quantum contextuality

Abstract

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).