On geometrical aspects of the graph approach to contextuality

TL;DR

This paper explores the geometric properties of contextuality in quantum theory using graph theory, introducing new quantifiers applicable to the exclusivity approach and enhancing the understanding of contextuality as a resource.

Contribution

It provides a geometric framework for contextuality, defines new quantifiers based on this geometry, and extends applicability to the exclusivity approach.

Findings

Geometric characterization of contextuality sets

Introduction of new geometric contextuality quantifiers

Applicability to the exclusivity approach

Abstract

The connection between contextuality and graph theory has led to many developments in the field. In particular, the sets of probability distributions in many contextuality scenarios can be described using well known convex sets from graph theory, leading to a beautiful geometric characterization of such sets. This geometry can also be explored in the definition of contextuality quantifiers based on geometric distances, which is important for the resource theory of contextuality, developed after the recognition of contextuality as a potential resource for quantum computation. In this paper we review the geometric aspects of contextuality and use it to define several quantifiers, which have the advantage of being applicable to the exclusivity approach to contextuality, where previously defined quantifiers do not fit.