# The contextual fraction as a measure of contextuality

## TL;DR

This paper introduces the contextual fraction as a comprehensive quantitative measure of contextuality in empirical models, linking it to Bell inequality violations, resource theories, and quantum computational advantages.

## Contribution

It formalizes the contextual fraction as a versatile measure, connecting it to various aspects of contextuality, including Bell inequalities, resource theories, and quantum information tasks.

## Key findings

- Provides a linear programming method to compute the measure.
- Establishes the measure's monotonicity under free operations.
- Demonstrates the measure's relevance to quantum computational advantages.

## Abstract

We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e. tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programming; it is monotone with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement based quantum computing.