Homotopical characterization of strongly contextual simplicial distributions on cone spaces

2023/11/23 by Aziz Kharoof, Kharoof, Aziz, Cihan Okay +1 · 1 citation
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Analysis #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2311.14111

openalex publication_date 2023/11/23 · openalex created_date 2023/11/28 · openalex updated_date 2026/07/28

Abstract

This paper offers a novel homotopical characterization of strongly contextual simplicial distributions with binary outcomes, specifically those defined on the cone of a 1-dimensional space. In the sheaf-theoretic framework, such distributions correspond to non-signaling distributions on measurement scenarios where each context contains 2 measurements with binary outcomes. To establish our results, we employ a homotopical approach that includes collapsing measurement spaces and introduce categories associated with simplicial distributions that can detect strong contextuality.

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• Polyhedral Classical Simulators for Quantum Computation

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