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arXiv · 2508.09711

Pretty good state transfer in Grover walks on abelian Cayley graphs

Koushik Bhakta·Bikash Bhattacharjya
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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.

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Koushik Bhakta, Bikash Bhattacharjya. 2025-08-13. Pretty good state transfer in Grover walks on abelian Cayley graphs. https://arxiv.org/abs/2508.09711

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