ALGEBRAIC COMBINATORICS

Pretty good quantum fractional revival in paths and cycles
Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 989-1004.

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.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.189
Classification: 05E30,  05C50,  33C05,  15A16,  81P40
Keywords: Fractional revival, state transfer, quantum, graph
Chan, Ada 1; Drazen, Whitney 2; Eisenberg, Or 3; Kempton, Mark 4; Lippner, Gabor 2

1 Department of Mathematics and Statistics York University Toronto ON Canada
2 Department of Mathematics Northeastern University Boston MA USA
3 Department of Mathematics Harvard University Cambridge MA USA
4 Department of Mathematics Brigham Young University Provo UT USA
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Chan, Ada; Drazen, Whitney; Eisenberg, Or; Kempton, Mark; Lippner, Gabor. Pretty good quantum fractional revival in paths and cycles. Algebraic Combinatorics, Volume 4 (2021) no. 6, pp. 989-1004. doi : 10.5802/alco.189. https://alco.centre-mersenne.org/articles/10.5802/alco.189/

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