Pretty good quantum state transfer in asymmetric graphs via potential

We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification...

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Bibliographic Details
Published inDiscrete mathematics Vol. 342; no. 10; pp. 2821 - 2833
Main Authors Eisenberg, Or, Kempton, Mark, Lippner, Gabor
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2019
Subjects
Cospectral
Quantum state transfer
Quantum walk
Quantum state transfer
Cospectral
Quantum walk
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Summary:We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification of the graph, along with a suitable potential, yields pretty good state transfer between the nodes. This generalizes previous work, concerning graphs with an involution, to asymmetric graphs.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2018.10.037