Laplacian pair state transfer in Q-graph

TL;DR

This paper investigates the conditions under which Laplacian perfect pair state transfer occurs in Q-graphs of regular graphs, providing new theoretical insights and criteria for such quantum state transfers.

Contribution

It characterizes when Laplacian perfect pair state transfer occurs in Q-graphs of regular graphs and offers a sufficient condition for pretty good pair state transfer.

Findings

Q-graph of an r-regular graph lacks Laplacian perfect pair state transfer if r+1 is prime or a power of 2

Provides a sufficient condition for Laplacian pretty good pair state transfer in Q-graphs

Advances understanding of quantum state transfer in graph-based quantum networks

Abstract

In 2018, Chen and Godsil proposed the concept of Laplacian perfect pair state transfer which is a brilliant generalization of Laplacian perfect state transfer. In this paper, we study the existence of Laplacian perfect pair state transfer in the Q-graph of an $r$-regular graph for $r\ge2$. We prove that the Q-graph of an $r$-regular graph does not have Laplacian perfect pair state transfer when $r+1$ is prime or a power of $2$. We also give a sufficient condition for Q-graph to have Laplacian pretty good pair state transfer.