Unifying Bell Inequalities and Entanglement Witnesses via Correlation Polytope Geometry — E8 Intelligence Research

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Buscemi's framework unifies Bell inequalities with entanglement witnesses through semidefinite programming and the facet structure of correlation polytopes, demonstrating that quantum violations correspond to specific geometric facets. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22294679

September 4, 2026Open Access

Unifying Bell Inequalities and Entanglement Witnesses via Correlation Polytope Geometry — E8 Intelligence Research

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Key Points

To establish a unified geometric framework that links Bell inequalities and entanglement witnesses using correlation polytopes and semidefinite programming.
Applied Buscemi's framework to map entanglement witnesses to Bell-type inequalities via quantum channel transformations.
Analyzed the facet structure of classical local hidden variable correlation polytopes against the larger convex set of quantum correlations using semidefinite programming.
Demonstrated that quantum violations of Bell inequalities map directly to specific geometric facets of the correlation polytope.
Characterized the Tsirelson bound of 2√2 for CHSH inequalities, defining the maximum quantum-to-classical correlation ratio of √2 (approximately 1.414).

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Implication

Theoretical analysis demonstrates geometric unification of Bell inequalities and entanglement witnesses across correlation polytopes, indicating quantum violations align with polytope facets.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9d1ee128139818eab22167 https://doi.org/10.5281/zenodo.22294679

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Unifying Bell Inequalities and Entanglement Witnesses via Correlation Polytope Geometry — E8 Intelligence Research

Key Points

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Implication

Discussion

Cite This Study

Unifying Bell Inequalities and Entanglement Witnesses via Correlation Polytope Geometry — E8 Intelligence Research

Key Points

No abstract yet

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Implication

Discussion

Cite This Study

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