{
  "abstract": "A Markov operator on a matrix algebra, that is, a unital completely positive map, is called positivity improving if it maps every nonzero positive element to an invertible one. This is the noncommutative counterpart of a stochastic matrix with strictly positive entries. We show that positivity improvement is self-dual and equivalent to a faithful quantum Markov--Dobrushin--Doeblin minorization. We also compare the scalar trace minorization with the optimal common-lower-bound construction of the quantum Markov--Dobrushin coefficient. We then characterize positivity improvement through the Kraus space of the map: a Markov operator is positivity improving if and only if the Hilbert--Schmidt orthogonal complement of its Kraus space contains no operator of rank one. As a consequence the Kraus rank of a positivity improving Markov operator on the algebra of $d\\times d$ matrices is at least $2d-1$, and an explicit Hankel-type channel shows that this bound is attained in every dimension. Although deciding positivity improvement is NP-hard in general, we obtain complete and effectively checkable classifications for qubits and qutrits, together with families of examples (Pauli, Weyl and Werner--Holevo channels) showing that all our estimates are optimal. Finally we show that, in infinite dimensions, positivity improvement no longer implies any contraction of the Markov operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.10042",
  "author_total": 2,
  "authors": [
    {
      "name": "Luigi Accardi"
    },
    {
      "name": "Abdessatar Souissi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mgrxkhtqgpc8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.10042",
  "fulltext_url": null,
  "id": "2mgrxkhtqgpc8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.10042",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.10042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mgrxkhtqgpc8.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:23Z",
      "native_id": "2611.10042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.10042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Positivity Improving Quantum Markov Operators",
  "title_text": "Positivity Improving Quantum Markov Operators",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/2mgrxkhtqgpc8",
  "venue": "arXiv",
  "versions": []
}