# Graph Approach to Extended Contextuality

## TL;DR

This paper extends the graph approach to contextuality, removing the nondisturbance assumption and providing new tools and conditions for analyzing contextuality in quantum measurements.

## Contribution

It introduces an extended definition of noncontextuality within the graph framework that does not rely on the nondisturbance assumption, broadening the scope of contextuality analysis.

## Key findings

- Extended graph-based framework for contextuality
- Conditions for testing contextuality without nondisturbance
- Compatibility with traditional noncontextuality when nondisturbance holds

## Abstract

Exploring the graph approach, we restate the extended definition of noncontextuality provided by the contextuality-by-default framework. This extended definition avoids the assumption of nondisturbance, which states that whenever two contexts overlap, the marginal distribution obtained for the intersection must be the same. We show how standard tools for characterizing contextuality can also be used in this extended framework for any set of measurements and, in addition, we also provide several conditions that can be tested directly in any contextuality experiment. Our conditions reduce to traditional ones for noncontextuality if the nondisturbance assumption is satisfied.