Asymmetric graphs with quantum symmetry

In recent years, a new interdisciplinary field of "quantum graph theory" has emerged, which studies quantum versions of graph-theoretic notions such as chromatic number, independent sets, and graph isomorphism. This provides a connection between the fields of graph theory, quantum information theory (QIT), and noncommutative geometry (NCG), leading to deep theorems and surprising results in each of these areas. In this talk, I will give an introduction to quantum isomorphisms and quantum automorphism groups, and I will outline a recent result in this field. Using techniques from QIT and group theory, I will construct graphs with trivial automorphism group but non-trivial quantum automorphism group, showing that even graphs with no symmetry at all can have hidden "quantum symmetry".

This talk is based on joint work with David E. Roberson (Technical University of Denmark) and Simon Schmidt (Ruhr University Bochum).