Perfect state transfer in NEPS of complete graphs

TL;DR

This paper investigates conditions under which NEPS of complete graphs exhibit perfect state transfer or periodicity, contributing to quantum information transfer understanding in graph-based quantum systems.

Contribution

It provides new sufficient conditions for NEPS of complete graphs to be periodic or have perfect state transfer, advancing quantum graph theory.

Findings

Identifies conditions for perfect state transfer in NEPS of complete graphs

Establishes criteria for periodicity in these graph structures

Enhances understanding of quantum state transfer in complex networks

Abstract

Perfect state transfer in graphs is a concept arising from quantum physics and quantum computing. Given a graph $G$ with adjacency matrix $A_G$, the transition matrix of $G$ with respect to $A_G$ is defined as $H_{A_{G}}(t) = \exp(-\mathrm{i}tA_{G})$, $t \in \mathbb{R},\ \mathrm{i}=\sqrt{-1}$. We say that perfect state transfer from vertex $u$ to vertex $v$ occurs in $G$ at time $\tau$ if $u \ne v$ and the modulus of the $(u,v)$-entry of $H_{A_G}(\tau)$ is equal to $1$. If the moduli of all diagonal entries of $H_{A_G}(\tau)$ are equal to $1$ for some $\tau$, then $G$ is called periodic with period $\tau$. In this paper we give a few sufficient conditions for NEPS of complete graphs to be periodic or exhibit perfect state transfer.