State Transfer on Mixed Graphs

Abstract

Mixed graphs, which generalize both undirected and directed graphs, provide a natural framework for investigating a broader class of quantum transport phenomena, including perfect state transfer ($\mathrm{PST}$) and multiple state transfer ($\mathrm{MST}$). The Hermitian adjacency matrix, incorporating both symmetric and asymmetric edge structures, establishes a unified spectral framework that reveals quantum phenomena absent in undirected graphs. In this paper, we study $\mathrm{PST}$ and $\mathrm{MST}$ on mixed graphs using the Hermitian adjacency matrix, extending results from undirected graphs and focusing on phenomena such as periodicity, one-way $\mathrm{PST}$, two-way $\mathrm{PST}$, and $\mathrm{MST}$. Additionally, we present novel results that contribute to a deeper understanding of quantum state transfer in mixed graphs.