Contextuality and Noncontextuality Measures and Generalized Bell Inequalities for Cyclic Systems

Abstract

Cyclic systems of dichotomous random variables have played a prominent role in contextuality research, describing such experimental paradigms as the Klyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg ones in physics, as well as conjoint binary choices in human decision making. Here, we understand contextuality within the framework of the Contextuality-by-Default (CbD) theory, based on the notion of probabilistic couplings satisfying certain constraints. CbD allows us to drop the commonly made assumption that systems of random variables are consistently connected. Consistently connected systems constitute a special case in which CbD essentially reduces to the conventional understanding of contextuality. We present a theoretical analysis of the degree of contextuality in cyclic systems (if they are contextual) and the degree of noncontextuality in them (if they are not). By contrast, all previously proposed measures of contextuality are confined to consistently connected systems, and most of them cannot be extended to measures of noncontextuality. Our measures of (non)contextuality are defined by the L_{1}-distance between a point representing a cyclic system and the surface of the polytope representing all possible noncontextual cyclic systems with the same single-variable marginals. We completely characterize this polytope, as well as the polytope of all possible probabilistic couplings for cyclic systems with given single-variable marginals.[...]

As pubished in Phys. Rev. A 101, 042119 (2020), but corrected in accordance with Erratum note in Physical Review A 101:069902, 2020 and Erratum note in Physical Review Review A Physical Review Review A 103:059901, 2021

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Cited by in corpus (10)

• Measures of Contextuality and Noncontextuality
• Assumption-free derivation of the Bell-type criteria of contextuality/nonlocality
• On the Quantum-like Contextuality of Ambiguous Phrases
• Contextuality Analysis of Impossible Figures
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Context-independent mapping and free choice are equivalent
• Varieties of contextuality based on probability and structural nonembeddability
• Contextuality and Informational Redundancy
• Contextuality and dichotomizations of random variables
• Quantum mechanics is compatible with counterfactual definiteness