Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction
For quantum foundations researchers, this work reframes contextuality as a limitation of classical representation at the subsystem level, offering a new perspective on the ontology of quantum theory.
The paper identifies an information-theoretic obstruction in classical single-state ontological models that reuse a fixed subsystem-level ontic state space, showing that the contextual information required is lower-bounded by conditional mutual information. This reveals a structural limitation of subsystem-level classical representation rather than a dualism about physical reality.
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 $I(C;O\mid λ)$ between intervention $C$ and outcome $O$ conditioned on the subsystem ontic state $λ$. 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.