Fractional revival on abelian Cayley graphs

2022/08/10 by Xiwang Cao, Gaojun Luo, Cao, Xiwang +1 · 1 citation
Computer Science · Physics and Astronomy · #05C25 #81P45 #81Q35 #Advanced Thermodynamics and Statistical Mechanics #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena

paper · pdf · doi:10.48550/arxiv.2208.05107

openalex publication_date 2022/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• State Transfer on Unitary Cayley Graphs and Quadratic Unitary Cayley Graphs

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