Epistemic Odds of Contextuality in Cyclic Systems

Abstract

Beginning with the Bell theorem, cyclic systems of dichotomous random variables have been the object of many foundational findings in quantum mechanics. Here, we ask the question: if one chooses a cyclic system "at random" (uniformly within the hyperbox of all possible systems with given marginals), what are the odds that it will be contextual? We show that the odds of contextuality rapidly tend to zero as the size of the system increases. The result is based on the Contextuality-by-Default theory, in which we do not have to assume that the systems are subject to the no-disturbance/no-signaling constraints.

arXiv comment7 pp, version 6 has a typo corrected, in press in European Physics Journal Special Topics

References in corpus (11)

• A simple test for hidden variables in spin-1 system
• Experimental non-classicality of an indivisible quantum system
• Condition for macroscopic realism beyond the Leggett-Garg inequalities
• All noncontextuality inequalities for the n-cycle scenario
• Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems
• Contextuality in Canonical Systems of Random Variables
• Proof of a Conjecture on Contextuality in Cyclic Systems with Binary Variables
• Probabilistic Foundations of Contextuality
• Measures of Contextuality and Noncontextuality
• On Joint Distributions, Counterfactual Values, and Hidden Variables in Relation to Contextuality
• Necessary Conditions for Extended Noncontextuality in General Sets of Random Variables