Fractional revival on abelian Cayley graphs

TL;DR

This paper characterizes when abelian Cayley graphs exhibit fractional revival, a quantum phenomenon, and provides new constructions and families of such graphs for quantum information applications.

Contribution

It offers a necessary and sufficient condition for fractional revival in abelian Cayley graphs and introduces new graph families with this property.

Findings

Characterization of fractional revival conditions

New constructions of abelian Cayley graphs with fractional revival

Identification of several new graph families with fractional revival

Abstract

Fractional revival, known as a quantum transport phenomenon, is essential for entanglement generation in quantum spin networks. The concept of fractional revival is a generalization of perfect state transfer and periodicity on graphs. In this paper, we propose a sufficient and necessary condition for abelian Cayley graphs having fractional revival between any two distinct vertices. With this characterization, two general constructions of abelian Cayley graphs having fractional revival is presented. Meanwhile, we establish several new families of abelian Cayley graphs admitting fractional revival.