Necessary and Sufficient Conditions for Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems

TL;DR

This paper establishes necessary and sufficient conditions for extended noncontextuality in various quantum systems, accounting for experimental biases and signaling, thus broadening the applicability of noncontextuality tests.

Contribution

It provides a comprehensive framework for determining extended noncontextuality in systems with inconsistent connectedness, including practical experimental scenarios.

Findings

Derived conditions for extended noncontextuality in diverse quantum systems.

Applied the conditions to analyze a real KCBS experiment.

Demonstrated the framework's relevance to real-world experimental data.

Abstract

The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements has a maximally noncontextual description if they can be imposed a joint distribution on in which the measurements of any one property in different contexts are equal to each other with the maximal probability allowed by their different distributions. We derive necessary and sufficient conditions for the existence of such a description in a broad class of systems including Klyachko-Can-Binicio\u{g}lu-Shumvosky-type (KCBS), EPR-Bell-type, and Leggett-Garg-type systems. Because these conditions allow for inconsistent connectedness, they are applicable to real experiments. We illustrate this by analyzing an experiment by Lapkiewicz and colleagues aimed at testing contextuality in a KCBS-type system.