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Algebraic Combinatorics

Pretty good fractional revival via diagonal perturbation: theory and examples

Whitney Drazen, Mark Kempton, Gábor Lippner

Published Oct 31, 2024• 0 citations
Publisher

Abstract

We develop the theory of pretty good quantum fractional revival in arbitrary sized subsets of a graph, including the theory for fractional cospectrality of subsets of arbitrary size. We use this theory to give conditions under which diagonal perturbation can induce pretty good fractional revival, and give several examples.
DOI
10.5802/alco.379

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We initiate the study of pretty good quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of pretty good fractional revival in a graph in terms of the eigenvalues and eigenvectors of the adjacency matrix of a graph. This characterization follows from a lemma due to Kronecker on Diophantine approximation, and is similar to the spectral characterization of pretty good state transfer in graphs. Using this, we give complete characterizations of when pretty good fractional revival can occur in paths and in cycles.
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