Perfect quantum state transfer of hard-core bosons on weighted path graphs

The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs using techniques in algebraic graph theory. The results suggest that hard-core bosons do not generically undergo PST, even on graphs which exhibit single-particle PST.