AI 中文总结
本文研究定向图上的真分数复兴存在性，建立定向图强共谱顶点间真FR的充要条件，证明阿贝尔群上定向Cayley图无真FR，并刻画阿贝尔群上定向半-Cayley图的真FR存在条件。
AI 中文摘要
分数复兴（FR）是完美状态转移（PST）的推广，是量子态转移中允许量子信息以一定概率在两个量子比特间传输的重要现象。FR的存在性已在多类图上被广泛研究，但定向图尚未被探讨。本文研究定向图上真FR的存在性，首先建立了定向图在强共谱顶点间允许真FR的充要条件；进一步证明阿贝尔群上的定向Cayley图不允许真FR，随后刻画了阿贝尔群上的定向半-Cayley图允许真FR的条件。
英文摘要
Fractional revival (FR), a generalization of perfect state transfer (PST), is a significant phenomenon in quantum state transfer that allows quantum information to be transmitted between two qubits with a certain probability. The existence of FR has been extensively studied on many classes of graphs. However, oriented graphs have not yet been investigated. In this paper, we investigate the existence of proper FR on oriented graphs. We first establish necessary and sufficient conditions for oriented graphs to admit proper FR between strongly cospectral vertices. Furthermore, we prove that oriented Cayley graphs over abelian groups do not admit proper FR, and we subsequently characterize the conditions under which oriented semi-Cayley graphs over abelian groups admit proper FR.
