Perfect and multiple state transfer in oriented Cayley graphs
Ada Chan, Venkata Raghu Tej Pantangi, Andriaherimanana Sarobidy Razafimahatratra, Peter Sin
TL;DR
This work develops a spectral-algebraic framework for PST and MST in oriented normal Cayley graphs, leveraging Bose–Mesner algebras and group characters. It proves general restrictions, notably that for solvable underlying groups PST-carrying sets satisfy $|\\mathcal{S}_e|\in\{2,3,4\}$ and rules out $|\\mathcal{S}_e|=6$, while providing explicit pst/mst criteria in terms of irreducible characters and central elements. The authors construct broad families of PST and MST examples across abelian, extraspecial $3$-groups, and nonsolvable groups, including small explicit groups and large families via wreath products, with key PST times such as $\tau=\frac{2\pi}{3\sqrt{3}}$ and $\tau=\frac{\pi}{4}$. These results yield practical pathways to engineer quantum transport on Cayley graphs and demonstrate how algebraic structure controls state-transfer feasibility and multiplicity. Overall, the paper advances both the theory and the repertoire of explicit, scalable PST/MST examples in oriented graph models relevant to quantum information transport.
Abstract
We study perfect state transfer and multiple state transfer in oriented normal Cayley graphs. We construct examples in a variety of groups, ranging from abelian to nonsolvable, and establish some general restrictions and nonexistence results.