Algebraic Graph Theory: Monogamy Violations in Perfect State Transfer

Talk by Sabrina Lato and Christino Tamon.

Continuous-time quantum walks on a graph are defined using a Hermitian matrix associated to a graph. For a quantum walk on a graph using either the adjacency matrix or the Laplacian, there can be perfect state transfer from a vertex to at most one other vertex in the graph. This monogamy property was proved by Kay for all real symmetric matrices. If a graph is associated with a Hermitian but not symmetric matrix, then we can still define a continuous-time quantum walk, but this monogamy property does not hold. In this talk, we will discuss graphs in violation with this property through examples, characterizations, and open questions.

This talk will largely be based on the following papers: