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:

Keywords: Fractional revival, state transfer, quantum, graph

^{1}; Drazen, Whitney

^{2}; Eisenberg, Or

^{3}; Kempton, Mark

^{4}; Lippner, Gabor

^{2}

@article{ALCO_2021__4_6_989_0, author = {Chan, Ada and Drazen, Whitney and Eisenberg, Or and Kempton, Mark and Lippner, Gabor}, title = {Pretty good quantum fractional revival in paths and cycles}, journal = {Algebraic Combinatorics}, pages = {989--1004}, publisher = {MathOA foundation}, volume = {4}, number = {6}, year = {2021}, doi = {10.5802/alco.189}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.189/} }

TY - JOUR TI - Pretty good quantum fractional revival in paths and cycles JO - Algebraic Combinatorics PY - 2021 DA - 2021/// SP - 989 EP - 1004 VL - 4 IS - 6 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.189/ UR - https://doi.org/10.5802/alco.189 DO - 10.5802/alco.189 LA - en ID - ALCO_2021__4_6_989_0 ER -

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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