{
  "abstract": "We study a variant of Schumacher compression. The task asks for the minimal memory cost for compressing many copies of a density matrix with known spectrum and unknown eigenbasis, without preserving its purification. For fixed dimension and distinct positive eigenvalues, we obtain the cost through its additive constant. Achievability uses a generalization of Werner's cloning map to $\\mathrm{GL}(d,\\mathbb C)$ irreducible representations, with finite trace-distance bounds controlled by highest-weight differences and row gaps. The matching converse follows from a quantitative form of Koashi--Imoto incompressibility for irreducible group orbits under a spectral-gap assumption. We also identify the relation between this quantum minimum description length and universal lossless coding overhead, and its connection to free entropy is explained in a companion letter. We provide a Lean certificate for our proofs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06742",
  "author_total": 4,
  "authors": [
    {
      "name": "Patrick Hayden"
    },
    {
      "name": "Alexander Maloney"
    },
    {
      "name": "Jinzhao Wang"
    },
    {
      "name": "Yuxiang Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cwhn0a1fd5zr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06742",
  "fulltext_url": null,
  "id": "4cwhn0a1fd5zr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06742",
  "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.IT"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220743771",
  "pdf_url": "https://arxiv.org/pdf/2610.06742",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cwhn0a1fd5zr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06742",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06742"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum minimum description of density matrices",
  "title_text": "Quantum minimum description of density matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/4cwhn0a1fd5zr",
  "venue": "arXiv",
  "versions": []
}