# Measures of Contextuality and Noncontextuality

## TL;DR

This paper introduces three measures of contextuality within the CbD framework, including a novel measure of noncontextuality, applicable to both consistent and inconsistent systems, advancing the quantification of contextuality.

## Contribution

The paper develops a new measure of noncontextuality and extends existing measures to inconsistent systems within the CbD framework, broadening the scope of contextuality quantification.

## Key findings

- Introduces a new measure of noncontextuality for the first time.
- Extends the contextual fraction measure to inconsistent systems.
- Shows limitations of existing measures in quantifying noncontextuality.

## Abstract

We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with "disturbance" allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of noncontextuality in noncontextual systems. The other two CbD-based measures do not suggest ways in which degree of noncontextuality of a noncontextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa, and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems.