Joint GOA/QLunch: Priyanga Ganesan

Speaker: Priyanga Ganesan, UC San Diego

Title: Quantum graphs and colorings

Abstract: In this talk, we will explore the interaction between operator algebras and quantum information theory through a discussion on quantum graphs. Quantum graphs are an operator generalization of classical graphs that have appeared in different branches of mathematics including operator algebras, non-commutative topology, operator systems theory and quantum information theory. I will present an overview of the theory of quantum graphs and discuss the connections
between different perspectives using operator algebraic methods. We will then investigate a coloring problem for quantum graphs using a quantum-input classical-output nonlocal game. Using this framework, we show that every quantum graph has a finite quantum coloring, but not necessarily finite classical coloring. We will develop a combinatorial characterization of quantum graph coloring using the winning strategies of this game and obtain various lower bounds for the chromatic numbers of quantum graphs.