In a continuous-time quantum walk on a network of qubits, pretty good state transfer is the phenomenon of state transfer between two vertices with fidelity arbitrarily close to 1. We construct families of graphs to demonstrate that there is no bound on the size of a set of vertices that admits pretty good state transfer between any two vertices of the set.

Mathematics Subject Classifications: 05C50, 05C38

Keywords: Continuous-time quantum walks, pretty good state transfer