{
  "abstract": "We show that one-way one-round quantum-LOCAL algorithms cannot $4$-color directed cycles with high probability. This is the first lower bound in the high-probability quantum LOCAL setting that goes beyond the non-signaling and bounded-dependence models, exploiting the structure of distributed quantum algorithms. Our proof establishes a bidirectional connection between distributed quantum computing and extremal combinatorics. We obtain our lower bound by proving a Mantel-type stability theorem for weighted matrix spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09091",
  "author_total": 2,
  "authors": [
    {
      "name": "Tom Gur"
    },
    {
      "name": "Longcheng Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jmty1zh874pk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09091",
  "fulltext_url": null,
  "id": "9jmty1zh874pk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09091",
  "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",
      "cs.DC"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212048109",
  "pdf_url": "https://arxiv.org/pdf/2609.09091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jmty1zh874pk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2609.09091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09091"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Impossibility of One-Way One-Round Quantum 4-Coloring via Matrix-Space Stability",
  "title_text": "Impossibility of One-Way One-Round Quantum 4-Coloring via Matrix-Space Stability",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/9jmty1zh874pk",
  "venue": "arXiv",
  "versions": []
}