Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910130827689984 |
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| author | Kim, Song-Ju |
| author_facet | Kim, Song-Ju |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16716 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction Kim, Song-Ju Artificial Intelligence Information Theory Quantum Physics 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. |
| title | Contextuality from Single-State Ontological Models: An Information-Theoretic Obstruction |
| topic | Artificial Intelligence Information Theory Quantum Physics |
| url | https://arxiv.org/abs/2602.16716 |