Bounds on quantum chromatic numbers for products of quantum graphs

We will provide a brief introduction to quantum graphs and quantum chromatic numbers, which are closely tied to quantum error-checking problems. Quantum graphs are a generalization of graphs using operator algebras, and quantum colorings are defined in terms of random strategies for non-local games using entanglement. We discuss existing bounds on quantum chromatic numbers and our work to expand upon these bounds. We define the lexicographic, cartesian, and categorical products of quantum graphs and investigate bounds on the resulting quantum chromatic number of these graph products. In particular, we define a quantum b-fold chromatic number which we use to derive bounds for the lexicographic product that are analogous to those in the classical case.

This is work done jointly with A. Meenakshi McNamara and Priyanga Ganesan.