Fundamentals of fractional revival in graphs

We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we determine when the adjacency algebra of a graph contains a matrix of a block diagonal form required for fractional revival, and introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of vertices. We give several constructions of graphs admitting fractional revival. This work resolves two open questions of Chan et al. (2019) [6].(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we determine the presence of a block diagonal matrix in the adjacency algebra of a graph, which is required for fractional revival, and introduce generalizations of cospectral and strongly cospectral vertices to arbitrary subsets of vertices. We provide several graph constructions that exhibit fractional revival, resolving two open questions from Chan et al. (2019) [6].