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

TL;DR

This paper investigates perfect quantum state transfer using discrete-time quantum walks on complete bipartite graphs, revealing conditions for perfect transfer depending on the positions and sizes of the graph parts.

Contribution

It demonstrates that perfect state transfer is achievable in complete bipartite graphs when sender and receiver are in the same part or in opposite parts with equal sizes.

Findings

Quantum walk dynamics are independent of the second part's size when sender and receiver are in the same part.

Perfect state transfer occurs only when sender and receiver are in opposite parts of equal size.

Achieves unit fidelity state transfer under specific graph configurations.

Abstract

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.