Pretty good state transfer in Grover walks on abelian Cayley graphs

• URL: http://arxiv.org/abs/2508.09711v1
• Date: Wed, 13 Aug 2025 11:03:25 GMT
• Title: Pretty good state transfer in Grover walks on abelian Cayley graphs
• Authors: Koushik Bhakta, Bikash Bhattacharjya,
• Abstract summary: We study pretty good state transfer (P GST) walks on graphs.<n>In general, we find a necessary and sufficient condition for the occurrence of P GST on graphs.<n>Our results yield infinite families of graphs that exhibit P GST but fail to exhibit perfect state transfer.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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