Pretty good quantum state transfer in symmetric spin networks via magnetic field.

*(English)*Zbl 1382.81049Summary: We study pretty good single-excitation quantum state transfer (i.e., state transfer that becomes arbitrarily close to perfect) between particles in symmetric spin networks, in the presence of an energy potential induced by a magnetic field. In particular, we show that if a network admits an involution that fixes at least one node or at least one link, then there exists a choice of potential on the nodes of the network for which we get pretty good state transfer between symmetric pairs of nodes. We show further that in many cases, the potential can be chosen so that it is only nonzero at the nodes between which we want pretty good state transfer. As a special case of this, we show that such a potential can be chosen on the endpoints of a spin chain to induce pretty good state transfer in chains of any length. This is in contrast to the result of the authors [“Perfect state transfer on graphs with a potential”, Quantum Inf. Comput. 17 No. 3, 303–327 (2017), arXiv:1611.02093], in which the authors show that there cannot be perfect state transfer in chains of length 4 or more, no matter what potential is chosen.

##### MSC:

81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |

78A25 | Electromagnetic theory (general) |

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\textit{M. Kempton} et al., Quantum Inf. Process. 16, No. 9, Paper No. 210, 23 p. (2017; Zbl 1382.81049)

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