Non-uniform Mixing in Continuous Quantum Walks
Christino Tamon · arXiv (Cornell University) · 2002
In this note, we study the mixing properties of continuous-time quantum random walks on graphs. We prove that the only graphs in the family of balanced complete multipartite graphs that have a uniform mixing property are $K_{2}$, $K_{3}$, $K_{4}$, and $K_{2,2}$. This is unlike the classical case where the uniform mixing property is satisfied by all such graphs. Our proof exploits the circulant structure of these graphs.