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

View PDF HTML (experimental) 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. Comments: Version 3: The main result was reframed as an information-theoretic obstruction rather than a no-go theorem. We clarified that ontic states are subsystem-level and reformulated interventions operationally to avoid dualism. The main claim was weakened to a proposition, restricting strict positivity to contextual regimes, with corresponding revisions to the abstract, intro, and appendix Subjects: Artificial Intelligence (cs.AI); Information Theory (cs.IT); Quantum Physics (quant-ph) Cite as: arXiv:2602.16716 [cs.AI] (or arXiv:2602.16716v3 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2602.16716 arXiv-issued DOI via DataCite Submission history From: Song-Ju Kim Dr. [view email] [v1] Tue, 3 Feb 2026 19:20:10 UTC (11 KB) [v2] Sat, 21 Feb 2026 02:25:37 UTC (11 KB) [v3] Wed, 15 Apr 2026 10:37:25 UTC (12 KB)