Perfect state transfer in NEPS of complete graphs

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 $H_{A_G}(t)=\exp (-\mathrm{i}t{A}_G)$, $t\in \mathbb{R},\mathrm{i}=\sqrt{-1}$. 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.

arXiv commentThis is the final version that will appear in Discrete Applied Mathematics

References in corpus (6)

• Quantum Communication Through an Unmodulated Spin Chain
• Perfect state transfer in quantum spin networks
• Quantum Networks on Cubelike Graphs
• Perfect state transfer in cubelike graphs
• Perfect state transfer on distance-regular graphs and association schemes
• Perfect State Transfer on NEPS of the path P3