Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction

TL;DR

This paper presents an information-theoretic obstruction to classical single-state ontological models reproducing quantum contextuality, highlighting limitations of subsystem-level classical representations.

Contribution

It introduces a lower bound on contextual information needed in classical models, connecting contextuality to conditional mutual information.

Findings

The lower bound is given by the conditional mutual information I(C;O|λ).

Shared-state reuse does not require full internalization of contextual distinctions.

The result clarifies limitations of subsystem-level classical representations.

Abstract

Contextuality is a central feature of quantum theory, traditionally understood as the impossibility of reproducing quantum measurement statistics using noncontextual ontological models. We study classical ontological descriptions in which a fixed subsystem-level ontic state space is reused across multiple interventions. Our main result is an information-theoretic obstruction: whenever a classical single-state model reproduces operational statistics using an auxiliary contextual register, the required contextual information is lower-bounded by the conditional mutual information $I(C;O\mid \lambda)$ between intervention $C$ and outcome $O$ conditioned on the subsystem ontic state $\lambda$. The mathematical inequality itself is elementary, but its interpretive significance is structural: under shared-state reuse, contextual distinctions need not be fully internalized within the subsystem ontic state alone. We provide a constructive illustration of this point and clarify how the issue should be understood as a limitation of subsystem-level classical representation, rather than as a dualism about physical reality. We further discuss how this perspective relates to ontological models and to contextuality in quantum foundations.