Department of mathematics

 

 

Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error capacity of quantum channels. Since then, quantum graph theory has become a field of study in its own right. Many definitions from classical graph theory, like colouring, connected components, and cliques have been generalised to the quantum case. A substantial source of difficulty in working with quantum graphs compared to classical graphs stems from the fact that they are no longer discrete objects. This makes it generally difficult to construct insightful, non-trivial examples. We present a collection of non-trivial quantum graphs that can be thought of in discrete terms, and that can be expressed in the diagrammatic formalism introduced by Musto, Reutter, and Verdon. The examples arise as the quantum graphs acted on by increasingly smaller classical matrix groups. We proceed to compute some of their graph-theoretic properties.