Quantum State Transfer on Coronas

TL;DR

This paper investigates how the corona product of graphs influences quantum state transfer, identifying conditions and constructing new graph families that exhibit state transfer properties.

Contribution

It introduces new conditions for state transfer in corona graphs and constructs novel graph families demonstrating this phenomenon, generalizing previous results.

Findings

Identified conditions for state transfer in corona graphs

Constructed new graph families with state transfer

Generalized known results on quantum walks

Abstract

We study state transfer in quantum walk on graphs relative to the adjacency matrix. Our motivation is to understand how the addition of pendant subgraphs affect state transfer. For two graphs $G$ and $H$, the Frucht-Harary corona product $G \circ H$ is obtained by taking $|G|$ copies of the cone $K_{1} + H$ and by connecting the conical vertices according to $G$. Our work explores conditions under which the corona $G \circ H$ exhibits state transfer. We also describe new families of graphs with state transfer based on the corona product. Some of these constructions provide a generalization of related known results.