Approximate quantum fractional revival in paths and cycles

• URL: http://arxiv.org/abs/2005.00492v1
• Date: Fri, 1 May 2020 17:07:17 GMT
• Title: Approximate quantum fractional revival in paths and cycles
• Authors: Ada Chan, Whitney Drazen, Or Eisenberg, Mark Kempton, Gabor Lippner
• Abstract summary: We give a complete characterization of approximate 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate 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 a complete characterizations of when approximate fractional revival can occur in paths and in cycles.

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