Perfect edge state transfer on abelian Cayley graphs.

Recently, perfect (quantum) edge state transfer (PEST, in short) was proposed as a potential model for quantum information processing. In a previous paper (X. Cao (2021) [12]), a characterization on cubelike graphs having PEST is presented. In this paper, a general characterization of abelian Cayley graphs having PEST is established by generalizing the main idea of the prior paper. Some concrete constructions of abelian Cayley graphs having PEST are provided. Additionally, some existence results are confirmed as well. Notably, we show that for every even number n , there is an abelian group G with order n , and a subset S in G such that Cay (G , S) has PEST at time π / 2. Particularly, we show that PEST may occur in some abelian Cayley graphs which don't exhibit perfect state transfer (PST). [ABSTRACT FROM AUTHOR]