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

arXiv:2602.16716v3 Announce Type: replace 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;Omid 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.

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Source: arXiv cs.AI | 2026-04-17