Minimal Kochen-Specker theorem in finite dimensions

TL;DR

This paper extends a minimal Kochen-Specker theorem to higher dimensions, providing experimentally testable inequalities that challenge non-contextual hidden variable models with fewer rays, thus advancing foundational quantum physics tests.

Contribution

It introduces a minimal, experimentally testable Kochen-Specker theorem in dimensions four and higher using fewer rays than previous proofs, strengthening the foundational constraints on hidden variable models.

Findings

Excludes NCHV models with minimal assumptions in dimensions ≥4

Uses the smallest known number of rays for such proofs

Provides state-independent inequalities for experimental tests

Abstract

In [1] we proved a strengthened Kochen-Specker theorem in 3 dimensions: non-contextual hidden variable (NCHV) models cannot reproduce all the quantum correlations of two compatible observables, which is a minimal requirement imposed on the NCHV models. Here we shall exclude the NCHV models with this minimal requirement in $d\ge 4$ dimensions by state-independent and experimentally testable inequalities satisfied by all NCHV models that are required to reproduce only the quantum correlations of at most two compatible observables. Furthermore our proofs use the smallest number of rays known so far, e.g., 25 (instead of 31) rays in $5$ dimensions and $5d-2\lfloor d/3\rfloor$ rays in $d\ge 6$ dimensions.