{
  "abstract": "Quantum tomography and quantum retrodiction are traditionally viewed as separate inference tasks. We show that the two are manifestations of the same underlying principle. We prove that the Petz recovery map of a measurement channel is a gradient of the log-likelihood used in maximum-likelihood tomography, and we derive its extension to arbitrary quantum channels. Consequently, for measurement channels, repeated applications of the Petz map monotonically increase the likelihood, naturally yielding a method for quantum tomography.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.23777",
  "author_total": 4,
  "authors": [
    {
      "name": "Sebastian Murk"
    },
    {
      "name": "Ian Tan"
    },
    {
      "name": "Fabian Müller"
    },
    {
      "name": "Dominik Šafránek"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/debdtwqwb4nb6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.23777",
  "fulltext_url": null,
  "id": "debdtwqwb4nb6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.23777",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
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      "arxiv",
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      "arxiv",
      "math.ST"
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      "1702|Quantum Information and Cryptography"
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  "openalex": "W7165749868",
  "pdf_url": "https://arxiv.org/pdf/2606.23777",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/debdtwqwb4nb6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2606.23777",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.23777"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Connecting Quantum Tomography and Quantum Retrodiction",
  "title_text": "Connecting Quantum Tomography and Quantum Retrodiction",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/debdtwqwb4nb6",
  "venue": "arXiv",
  "versions": []
}