Maximally epistemic interpretations of the quantum state and contextuality

TL;DR

This paper explores the deep connection between quantum contextuality and maximally epistemic models of the quantum state, showing that certain noncontextuality assumptions imply the impossibility of such models, thus linking foundational quantum theorems.

Contribution

It demonstrates that preparation noncontextual models must be maximally epistemic and Kochen-Specker noncontextual, providing new insights into quantum foundations and the implications of contextuality.

Findings

Preparation noncontextual models are maximally epistemic.

Kochen-Specker theorem implies the impossibility of maximally epistemic models.

The results connect contextuality with Bell's theorem via an EPR-like argument.

Abstract

We examine the relationship between quantum contextuality (in both the standard Kochen-Specker sense and in the generalised sense proposed by Spekkens) and models of quantum theory in which the quantum state is maximally epistemic. We find that preparation noncontextual models must be maximally epistemic, and these in turn must be Kochen-Specker noncontextual. This implies that the Kochen-Specker theorem is sufficient to establish both the impossibility of maximally epistemic models and the impossibility of preparation noncontextual models. The implication from preparation noncontextual to maximally epistemic then also yields a proof of Bell's theorem from an EPR-like argument.