Perfect state transfer by means of discrete-time quantum walk on complete bipartite graphs

We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part of the graph is considered. We show that in this case the dynamics of the quantum walk is independent of the size of the second part and reduces to the one for the star graph where perfect state transfer is achieved. Second, we consider the situation where the sender and the receiver vertex are in the opposite parts of the graph. In such a case, the state transfer with unit fidelity is achieved only when the parts have the same size.