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Pretty good quantum state transfer in asymmetric graphs via potential. (English) Zbl 1417.05172
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.

05C75 Structural characterization of families of graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
Full Text: DOI arXiv
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