Perfect state transfer on Cayley graphs over dihedral groups

Abstract

Recently, there are extensive studies on perfect state transfer on graphs due to their significant applications in quantum information processing and quantum computations. However, most of the graphs previously investigated are abelian Cayley graphs. In this paper, we study perfect state transfer on Cayley graphs over dihedral groups. Using the representations of the dihedral group , we present some necessary and sufficient conditions for the Cayley graph to have a perfect state transfer between two distinct vertices for some connection set S. Based on these conditions, we show that cannot have PST if n is odd and S is conjugation-closed. For some even integers n, it is possible for to have PST, some concrete constructions are provided.

COMMUNICATED BY:

• J. Y. Shao

Keywords:

• Perfect state transfers
• Cayley graphs
• eigenvalues of a graph
• dihedral groups

Acknowledgments

The authors would like to express their grateful thankfulness to the referee for their valuable comments and suggestions. X. Cao would like to thank the Institute of Mathematics, Academia Sinica for the financial support during his visiting.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

X. Cao's work is supported by the National Natural Science Foundation of China (11771007, 61572027). Keqin Feng's work is supported by the National Natural Science Foundation of China (11471178, 11571107) and the Tsinghua National Information Science and Technology Lab.