Pretty good state transfer in Grover walks on abelian Cayley graphs
Combinatorics
2025-08-14 v1 Quantum Physics
Abstract
In this paper, we study pretty good state transfer (PGST) in Grover walks on graphs. We consider transfer of quantum states that are localized at the vertices of a graph and we use Chebyshev polynomials to analyze PGST between such states. In general, we find a necessary and sufficient condition for the occurrence of PGST on graphs. We then focus our analysis on abelian Cayley graphs and derive a necessary and sufficient condition for the occurrence of PGST on such graphs. Consequently, we obtain a complete characterization of PGST on unitary Cayley graphs. Our results yield infinite families of graphs that exhibit PGST but fail to exhibit perfect state transfer.
Keywords
Cite
@article{arxiv.2508.09711,
title = {Pretty good state transfer in Grover walks on abelian Cayley graphs},
author = {Koushik Bhakta and Bikash Bhattacharjya},
journal= {arXiv preprint arXiv:2508.09711},
year = {2025}
}