Quantum state transfer between twins in weighted graphs

Stephen Kirkland, Hermie Monterde, Sarah Plosker

Published 2022-01-08, updated 2022-08-23Version 2

Twin vertices in simple unweighted graphs are vertices that have the same neighbours and, in the case of weighted graphs with possible loops, corresponding edges have equal weights. In this paper, we explore the role of twin vertices in quantum state transfer. In particular, we provide a characterization of periodicity, perfect state transfer, pretty good state transfer between twin vertices in a weighted graph with respect to its adjacency, Laplacian and signless Laplacian matrices. As an application, we characterize all simple unweighted double cones on regular graphs that exhibit periodicity, perfect state transfer, and pretty good state transfer.