Necessary Conditions for Extended Noncontextuality in General Sets of Random Variables

TL;DR

This paper reformulates the extended definition of noncontextuality using graph theory, deriving necessary conditions that can be experimentally tested without assuming perfect non-disturbance, thus broadening the applicability of contextuality tests.

Contribution

It introduces a graph-theoretical framework for extended noncontextuality, providing necessary conditions that do not rely on the non-disturbance assumption, applicable to real experimental data.

Findings

Derived necessary conditions for extended noncontextuality based on graph geometry

Conditions reduce to traditional noncontextuality criteria under non-disturbance

Framework applicable to any set of random variables in contextuality experiments

Abstract

We explore the graph approach to contextuality to restate the extended definition of noncontextuality as given by J. Kujala et. al. [Phys. Rev. Lett. 115, 150401 (2015)] using graph-theoretical terms. This extended definition avoids the assumption of the pre-sheaf or non-disturbance condition, which states that if two contexts overlap, then the marginal distribution obtained for the intersection must be the same, a restriction that will never be perfectly satisfied in real experiments. With this we are able to derive necessary conditions for extended noncontextuality for any set of random variables based on the geometrical aspects of the graph approach, which can be tested directly with experimental data in any contextuality experiment and which reduce to traditional necessary conditions for noncontextuality if the non-disturbance condition is satisfied.