An explicit contextualized hidden variable model replicating an indivisible quantum system

TL;DR

This paper constructs a hidden variable model that exactly reproduces quantum contextuality bounds for a spin-1 system, highlighting differences from entangled spin-1/2 particles and advancing understanding of quantum contextuality.

Contribution

It introduces a explicit contextualized hidden variable model that replicates quantum bounds for a spin-1 system under relaxed non-contextuality assumptions.

Findings

The model reproduces the quantum bound for the Pentagram inequality.

Relaxed non-contextuality assumptions enable classical replication of quantum contextuality.

Differences between spin-1 and spin-1/2 systems in hidden variable models are discussed.

Abstract

Recent experiments and theory have further illuminated the concept of "quantum contextuality". In this paper we take an inequality - the Pentagram (or KCBS) inequality, which is violated by an unentangled spin-1 system - and given a relaxed assumption of non-contextuality show that a hidden variable model may be constructed that replicates exactly the quantum bound. This is in contrast to the case of an entangled pair of spin-1/2 particles where a similar relaxation of the assumption of locality does not lead to a replication of the quantum bound. Some reasons are proposed for why this may be the case.