{
  "abstract": "We completely classify connected Cayley graphs over finite abelian groups that exhibit perfect state transfer in Grover walks. First, we show that a Cayley graph over any finite group exhibiting perfect state transfer has valency $1$, $2$, or $4$. For valency $4$, we prove that an abelian Cayley graph $\\operatorname{Cay}(Γ,S)$ exhibits perfect state transfer if and only if $S=\\{a,-a,a+h,-a+h\\}$, where $h$ has order $2$, and $4\\nmid |Γ|/2$. Combining this characterization with the valency-one and valency-two cases, we explicitly determine all pairs $(Γ,S)$ for which $\\operatorname{Cay}(Γ,S)$ exhibits perfect state transfer. Our results extend the classification of circulant graphs of valency at most four obtained by Kubota and Yoshino [Circulant graphs with valency up to 4 that admit perfect state transfer in Grover walks, \\emph{J. Comb. Theory Ser. A.}, 216 (2025) 106064] to Cayley graphs over arbitrary finite abelian groups and to all valencies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21946",
  "author_total": 2,
  "authors": [
    {
      "name": "Koushik Bhakta"
    },
    {
      "name": "Bikash Bhattacharjya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dc2t51fzehfcs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21946",
  "fulltext_url": null,
  "id": "dc2t51fzehfcs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21946",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7222727177",
  "pdf_url": "https://arxiv.org/pdf/2610.21946",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dc2t51fzehfcs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21946",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21946"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A complete classification of perfect state transfer in Grover walks on abelian Cayley graphs",
  "title_text": "A complete classification of perfect state transfer in Grover walks on abelian Cayley graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/dc2t51fzehfcs",
  "venue": "arXiv",
  "versions": []
}