Perfect State Transfer on Weighted Abelian Cayley Graphs*

Citation:

Xiwang CAO,Keqin FENG,Ying-Ying TAN.Perfect State Transfer on Weighted Abelian Cayley Graphs*[J].Chinese Annals of Mathematics B,2021,42(4):625~642
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Authors:

Xiwang CAO; Keqin FENG;Ying-Ying TAN

Foundation:

National Natural Science Foundation of China (Nos. 11771007,11601003, 11801007, 12031011) and Natural Science Foundation of Anhui Province (No. 1808085MA17).
Abstract: Recently, there are extensive studies on perfect state transfer (PST for short) on graphs due to their significant applications in quantum information processing and quantum computations. However, there is not any general characterization of graphs that have PST in literature. In this paper, the authors present a depiction on weighted abelian Cayley graphs having PST. They give a unified approach to describe the periodicity and the existence of PST on some specific graphs.

Keywords:

Perfect state transfer, Cayley graph, Eigenvalues of a graph, Weighted graph, Random walk

Classification:

05C25, 81P45, 81Q35
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