{
  "abstract": "Godsil and McKay (1978) showed that the rooted product is a powerful tool for constructing non-isomorphic cospectral pairs of graphs. Despite lacking a convenient tensor product structure, we show that the rooted product is useful for constructing graphs with good quantum state transfer properties. In particular, we prove a simple transference principle: if a graph $X$ has quantum state transfer and $Y$ is a controllable graph, their rooted product $X^Y$ has quantum state transfer (inherited from $X$). This complements a folklore property of Cartesian product which preserves perfect state transfer. However, the rooted product is a significantly sparser graph and, more importantly, can be easily used to construct efficient high-fidelity state transfer even if $X$ has no quantum state transfer. Our proof exploits the fact that a rooted product creates a large number of strongly cospectral pairs of vertices and that its condition number can be controlled by its pendant subgraph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14537",
  "author_total": 3,
  "authors": [
    {
      "name": "Addison Ballif"
    },
    {
      "name": "Christino Tamon"
    },
    {
      "name": "Gabriel Tucker"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1adcv4zxxc9x1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14537",
  "fulltext_url": null,
  "id": "1adcv4zxxc9x1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14537",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7213293356",
  "pdf_url": "https://arxiv.org/pdf/2609.14537",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1adcv4zxxc9x1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14537",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14537"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Controlling quantum state transfer in rooted products",
  "title_text": "Controlling quantum state transfer in rooted products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/1adcv4zxxc9x1",
  "venue": "arXiv",
  "versions": []
}