Contextuality as an Information-Theoretic Obstruction to Classical Probability

TL;DR

The paper reframes contextuality as an information-theoretic obstruction under a single-state semantics constraint, formalized by $I(S;C)=0$. It shows that reproducing contextual statistics within a classical model necessitates either embedding contextual information in the internal state ($I(S;C)>0$) or externalizing it via a memory label with $H(M) \ge I(S;C)$. This externalization yields a nonzero information cost, reframing contextuality as a resource constraint rather than a binary quantum/classical distinction. The result clarifies why quantum probability naturally supports contextual operations without explicit contextual encoding and sets the stage for future quantitative analyses of $I(S;C)$ in contextual scenarios.

Abstract

Contextuality is a central feature distinguishing quantum from classical probability theories, yet its operational meaning remains subject to interpretation. We reconsider contextuality from an information-theoretic perspective, focusing on operational models constrained to maintain a single internal state with fixed semantics across multiple contexts. Under this constraint, we show that contextual statistics certify an unavoidable obstruction to classical probabilistic descriptions. Specifically, any classical model that reproduces such statistics must either embed contextual dependence into the internal state or introduce additional external labels carrying nonzero information. This result identifies contextuality as a witness of irreducible information cost in classical representations, rather than as a purely nonclassical anomaly. From this viewpoint, quantum probability emerges as a canonical framework that accommodates contextual operations without requiring explicit contextual encoding.