QLunch: Larissa Kroell

Title: Regularity for Quantum Graphs

Abstract: In 2010, Duan, Severini and Winter introduced quantum graphs as a tool to study zero-error communication via quantum channels. Since then, three equivalent perspectives emerged: a quantization of the edge relation giving an operator system viewpoint, a quantization of the adjacency matrix leading to the definition of quantum Schur-idempotents, and the quantum edge projection, which also gives a translation between perspectives. A natural question to ask is which properties of graphs generalize to the quantum setting. In this talk, we will focus on the property of regularity. After an overview of the different perspectives, we define regularity for quantum graphs and discuss properties of the regularity constant. This is joint work with Matthew Kennedy and Junichiro Matsuda.