Fractional revival on quasi-abelian Cayley graphs

TL;DR

This paper characterizes when quasi-abelian Cayley graphs exhibit fractional revival, a quantum phenomenon important for entanglement, extending previous results from abelian to quasi-abelian groups.

Contribution

It provides a necessary and sufficient condition for fractional revival in quasi-abelian Cayley graphs, broadening the understanding beyond abelian groups.

Findings

Established a criterion for fractional revival in quasi-abelian Cayley graphs.

Extended previous results from abelian to quasi-abelian group structures.

Contributed to quantum network design by characterizing quantum transport phenomena.

Abstract

Fractional revival, a quantum transport phenomenon critical to entanglement generation in quantum spin networks, generalizes the notion of perfect state transfer on graphs. A Cayley graph $\mathrm{Cay}(G,S)$ is called quasi-abelian if its connection set $S$ is a union of conjugacy classes of the group $G$. In this paper, we establish a necessary and sufficient condition for quasi-abelian Cayley graphs to have fractional revival. This extends a result of Cao and Luo (2022) on the existence of fractional revival in Cayley graphs over abelian groups.