{
  "abstract": "Graph theory is a powerful tool in quantum computing, with applications ranging from quantum circuit synthesis and optimization to entanglement mapping. Recent work has shown how one can use edge-colored graphs to model photonic experiments that generate GHZ and W states. However, the latter work also proved that verifying that a graph models a Dicke state experiment is coNP-complete. In this work, we provide families of graphs that generate $|D_{k}^a\\rangle \\otimes |0\\rangle^{\\otimes b }$, where $b = |a-2k|$ is the number of spectator modes. The graph setup consists of a doubled complete subgraph on $a$ vertices and a collection of auxiliary vertices. We prove that every coincidence carries exactly $k$ excitations, every weight-$k$ computational basis state on bitstrings of length $a$ is realized, and each of those bitstrings is realized exactly $(n/2)!$ times, where $n = a+b$. Since verifying the Dicke FORALL condition is coNP-complete in general, constructing explicit families that provably generate Dicke states is of interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22564",
  "author_total": 1,
  "authors": [
    {
      "name": "Rebekah Herrman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae11dpwqs4dt7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22564",
  "fulltext_url": null,
  "id": "ae11dpwqs4dt7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22564",
  "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",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214056584",
  "pdf_url": "https://arxiv.org/pdf/2609.22564",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae11dpwqs4dt7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.22564",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22564"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Generating Dicke State Graphs",
  "title_text": "Generating Dicke State Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/ae11dpwqs4dt7",
  "venue": "arXiv",
  "versions": []
}