Cayley graphs of dihedral groups having perfect edge state transfer

Abstract

Perfect state transfer plays a crucial role in quantum information processing and quantum computation. However, perfect state transfer is a rare phenomenon. As a generalization of perfect state transfer, perfect edge state transfer overcomes this disadvantage and there are more graphs admitting perfect edge state transfer than admitting perfect state transfer. In this paper, we reveal the relations between perfect state transfer and perfect edge state transfer on Cayley graphs. Furthermore, we present necessary and sufficient conditions for the existence of perfect edge state transfer on Cayley graphs of dihedral groups. With these conditions, several concrete constructions of Cayley graphs admitting perfect edge state transfer are proposed. Notably, this is the first attempt at perfect edge state transfer on Cayley graphs.