A game-theoretic probability approach to loopholes in CHSH experiments
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| author | Nomura, Takara Yamagata, Koichi Fujiwara, Akio |
| author_facet | Nomura, Takara Yamagata, Koichi Fujiwara, Akio |
| contents | We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice'') loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature's hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09339 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A game-theoretic probability approach to loopholes in CHSH experiments Nomura, Takara Yamagata, Koichi Fujiwara, Akio Quantum Physics Computer Science and Game Theory Probability We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice'') loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature's hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations. |
| title | A game-theoretic probability approach to loopholes in CHSH experiments |
| topic | Quantum Physics Computer Science and Game Theory Probability |
| url | https://arxiv.org/abs/2601.09339 |