The goal of quantum communication is to transmit information with a high level of accuracy, or fidelity. Ideally, we achieve perfect state transfer, which occurs when the fidelity is 1. Since examples of perfect state transfer are rare, we relax our requirement to that of pretty good state transfer, which occurs when fidelities arbitrarily close to 1 can be achieved. We consider a continuous time quantum walk on an unweighted path on n vertices, to which a loop of weight w has been added at each end vertex. We demonstrate a dense set of weights for which pretty good state transfer cannot be achieved, highlighting the precision required in setting the weights to achieve pretty good state transfer.

This talk is based on joint work with Steve Kirkland.