The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer.
QUANTUM GROUPS, QUANTUM FOUNDATIONS, AND QUANTUM INFORMATION: A FESTSCHRIFT FOR TONY SUDBERY
, Article 012012. 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.
|Title:||The 3-dimensional cube is the only periodic, connected cubic graph with perfect state transfer|
|Location:||Univ York, York, ENGLAND|
|Open access status:||An open access publication|
|UCL classification:||UCL > School of BEAMS > Faculty of Engineering Science > Computer Science|
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