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

Abstract

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.

15 pages, 5 EPS figures; the main result is now weaker because of an error in the previous version. I would like to thank Matthew Russell for pointing out the error to me

References in corpus (3)

• Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Quantum Networks on Cubelike Graphs

Cited by in corpus (1)

• The Basics of Perfect Communication through Quantum Networks