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

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