Title: Monogamy Violations in Perfect State Transfer
|Speakers:||Sabrina Lato & Christino Tamon|
|Affiliations:||University of Waterloo & Clarkson Unversity|
|Zoom:||Contact Soffia Arnadottir|
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.