Unifying Bell Inequalities via Polytopes and Quantum Communication Advantages — E8 Intelligence Research

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Bell inequalities can be unified via a generalized framework where quantum entanglement and nonlocality emerge from a single polytope structure, with their violations directly tied to communication complexity advantages. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22469849

September 6, 2026Open Access

Unifying Bell Inequalities via Polytopes and Quantum Communication Advantages — E8 Intelligence Research

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Key Points

To establish a unified geometric framework that links Bell inequalities, quantum nonlocality, and entanglement to polytope structures and quantum communication advantages.
Represented Bell inequalities as facets of the local probability polytope formed by convex combinations of factorizable conditional probabilities.
Analyzed nonlocal games comparing quantum winning probabilities against classical winning probabilities.
Characterized polytope facet geometries through probability simplex dimensions, correlation matrix rank, and type A_n root systems.
Demonstrated that quantum strategy advantages over classical limits are bounded by the Grothendieck constant (1.676 ≤ K_G ≤ 1.782) for correlation-type inequalities.
Identified that Clauser-Horne-Shimony-Holt inequality facet structures adhere to the maximal Tsirelson quantum bound of 2√2.

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Implication

Theoretical analysis demonstrates unification of Bell inequalities within a single polytope framework, indicating fundamental bounds on quantum communication advantages.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9fd76758e84d0ff5b46133 https://doi.org/10.5281/zenodo.22469849

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Unifying Bell Inequalities via Polytopes and Quantum Communication Advantages — E8 Intelligence Research

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Discussion

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Unifying Bell Inequalities via Polytopes and Quantum Communication Advantages — E8 Intelligence Research

Key Points

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Implication

Discussion

Cite This Study

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