On state transfer in Cayley graphs for abelian groups

TL;DR

This paper characterizes perfect quantum state transfer in Cayley graphs of abelian groups with cyclic Sylow-2-subgroups, extending previous results from cyclic groups to a broader class of abelian groups.

Contribution

It generalizes Bašić's 2013 characterization of perfect state transfer from cyclic groups to abelian groups with cyclic Sylow-2-subgroups.

Findings

Provides necessary and sufficient conditions for perfect state transfer in these Cayley graphs.

Extends the understanding of quantum state transfer in algebraic graph structures.

Broadens the class of groups where perfect state transfer can be characterized.

Abstract

In this paper, we characterize perfect state transfer in Cayley graphs for abelian groups that have a cyclic Sylow-2-subgroup. This generalizes a result of Ba\v{s}i\'c from 2013 where he provides a similar characterization for Cayley graphs of cyclic groups.