Quantum chromatic numbers via operator systems

TL;DR

This paper introduces new quantum chromatic numbers for graphs, characterizes them using operator system tensor products, and explores their relationships with existing graph parameters and non-signalling correlations.

Contribution

It defines novel quantum chromatic numbers, links them to operator system tensor products, and compares them with known graph parameters and non-signalling correlations.

Findings

Established inequalities between new quantum chromatic numbers and existing graph parameters.

Linked quantum chromatic numbers to non-signalling correlation boxes.

Provided characterizations of quantum chromatic numbers via operator system tensor products.

Abstract

We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the literature and exhibit a link between them and non-signalling correlation boxes.