{
  "abstract": "The quantum Hamming bound arises from a direct dimension estimate for exact quantum error-correcting codes. For nondegenerate codes, distinct correctable errors map the code space into orthogonal subspaces, so dimension counting directly gives the bound; degeneracy allows these subspaces to overlap and invalidates the argument. Although linear-programming, asymptotic, and structural approaches have advanced the problem from several directions, the general local-dimension case has remained open. Here we prove the quantum Hamming bound for every local dimension $q\\ge3$. Building on the exact two-center Fourier reduction, we develop new overlap estimates for nonbinary Hamming spaces. For $q\\ge4$, Jacobi estimates and monotonicity give a uniform gap; qutrits form the boundary case where the gap vanishes and are handled by a filtered correction. This completes the finite-length nonbinary case; together with the existing qubit result, it establishes the quantum Hamming bound for arbitrary local dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.22538",
  "author_total": 2,
  "authors": [
    {
      "name": "Yu-Xuan Zhang"
    },
    {
      "name": "Jing-Ling Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bj7p25c2bv8zz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.22538",
  "fulltext_url": null,
  "id": "bj7p25c2bv8zz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.22538",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7165668711",
  "pdf_url": "https://arxiv.org/pdf/2606.22538",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bj7p25c2bv8zz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2606.22538",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.22538"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Quantum Hamming Bound in Arbitrary Local Dimension",
  "title_text": "The Quantum Hamming Bound in Arbitrary Local Dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/bj7p25c2bv8zz",
  "venue": "arXiv",
  "versions": []
}