Title: Quantum walks do not like bridges
|Affiliation:||Universidade Federal de Minas Gerais|
|Zoom:||Contact Sabrina Lato|
In this talk we consider graphs with two cut vertices joined by a bridge, and prove that there can be no quantum perfect state transfer between these vertices, unless the graph has no other vertex. We achieve this result by applying the 1-sum lemma for the characteristic polynomial of graphs, the neutrino identities that relate entries of eigenprojectors and eigenvalues, and variational principles for eigenvalues (Cauchy interlacing and Weyl inequalities).