The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer

Details The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer

2010-01-05

arxiv.org/abs/1001.0674v2

2010 J. Phys.: Conf. Ser. 254 012012

Physics

Quantum Physics

15 pages, 5 EPS figures; the main result is now weaker because of an error in the previous version. I would like to thank Matt

Scientific paper

10.1088/1742-6596/254/1/012012

There is perfect state transfer between two vertices of a graph, if a single excitation can travel with fidelity one between the corresponding sites of a spin system modeled by the graph. When the excitation is back at the initial site, for all sites at the same time, the graph is said to be periodic. A graph is cubic if each of its vertices has a neighbourhood of size exactly three. We prove that the 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer. We conjecture that this is also the only connected cubic graph with perfect state transfer.

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