State transfer on graphs

If X is a graph with adjacency matrix A, then we define H(t) to be the operator exp(itA). We say that we have perfect state transfer in X from the vertex u to the vertex v at time τ if the uv-entry of |H(τ)u,v|=1. State transfer has been applied to key distribution in commercial cryptosystems, and i...

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Bibliographic Details
Published inDiscrete mathematics Vol. 312; no. 1; pp. 129 - 147
Main Author Godsil, Chris
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.01.2012
Subjects
Continuous quantum walk
Graph spectra
Graphs
Mathematical analysis
Operators
Perfect state transfer
Perfect state transfer
Graph spectra
Continuous quantum walk
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Summary:If X is a graph with adjacency matrix A, then we define H(t) to be the operator exp(itA). We say that we have perfect state transfer in X from the vertex u to the vertex v at time τ if the uv-entry of |H(τ)u,v|=1. State transfer has been applied to key distribution in commercial cryptosystems, and it seems likely that other applications will be found. We offer a survey of some of the work on perfect state transfer and related questions. The emphasis is almost entirely on the mathematics. ► We survey the interactions between graph theory and perfect state transfer. ► Perfect state transfer is of interest in quantum computing. ► We include some new results and open questions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2011.06.032