{
  "abstract": "We study general $(r,δ)$-quantum locally recoverable codes (qLRCs) without assuming purity or a stabilizer structure, and with arbitrarily overlapping recovery blocks. Using a selection lemma for multiple-erasure recovery, we establish a Singleton-like upper bound for general quantum subspaces. When $δ=2$, this bound reduces to the general single-erasure bound of Golowich and Guruswami. An integer optimization yields an explicit remainder correction that tightens the bound by up to $δ-2$. For pure codes, local decoupling and entropy arguments extend the parameter bound of Galindo et al., originally obtained for pure stabilizer codes constructed from Euclidean or Hermitian dual-containing classical codes, to arbitrary pure quantum subspaces. We also remove the partition assumption from several existing pure-code bounds for disjoint recovery blocks and obtain a further remainder correction by optimizing the budget. Finally, we analyze three families attaining these bounds: pure codes with overlapping recovery blocks and $d=δ$, which exhibit both a strict improvement of the pure-code bound and simultaneous equality in the pure-code and general bounds; impure codes with disjoint recovery blocks attaining the general bound; and an existing family of pure codes with overlapping recovery blocks and $d>δ$, which simultaneously attains all these bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40273",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuowei Ma"
    },
    {
      "name": "Fei Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0pr0gena2epfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40273",
  "fulltext_url": null,
  "id": "0pr0gena2epfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40273",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40273",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0pr0gena2epfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40273",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40273"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Bounds for General $(r,δ)$-Quantum Locally Recoverable Codes",
  "title_text": "Bounds for General (r,δ)-Quantum Locally Recoverable Codes",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:47Z",
  "url": "https://research.draconitic.com/paper/0pr0gena2epfg",
  "venue": "arXiv",
  "versions": []
}