Degrees, Levels, and Profiles of Contextuality

TL;DR

This paper introduces the concept of a contextuality profile, a curve representing the degree of contextuality at various levels of variable consideration, providing a nuanced analysis beyond a single measure.

Contribution

It proposes a new framework for analyzing contextuality through profiles and introduces a method for systematic exploration using concatenated systems.

Findings

The contextuality profile can be characterized at different levels of variable consideration.

The method applies to multiple existing measures of contextuality.

Systematic analysis reveals detailed insights into the structure of contextuality.

Abstract

We introduce a new notion, that of a contextuality profile of a system of random variables. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered. A system is represented at level n if one only considers the joint distributions with no more than n variables, ignoring higher-order joint distributions. We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality. We present a method of concatenated systems to explore contextuality profiles systematically, and we apply it to the contextuality profiles for three major measures of contextuality proposed in the literature.