{
  "abstract": "The Petz recovery map provides a near optimal decoder for approximate quantum error correction, but its inverse square-root normalization complicates circuit implementation. We use the polar structure of the Petz recovery isometry to implement recovery through a single quantum singular value transformation (QSVT). We give explicit block-encoding circuits and an extended recovery isometry that yields approximate Petz recovery without postselection. We bound the diamond distance between the approximate and ideal Petz encoding-recovery channels in terms of a spectrum-weighted loss, which provides a channel specific objective for optimizing the QSVT angles. Uniform polynomial approximation yields an asymptotic error bound that decays exponentially with the number of QSVT iterations, at a rate controlled by the smallest nonzero scaled singular value. Applications to Haar-random encoding and the Hayden-Preskill protocol illustrate the tradeoff between circuit depth and recovery accuracy and place existing scrambling decoders within a common Petz recovery framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20515",
  "author_total": 2,
  "authors": [
    {
      "name": "Hanzhang Zhao"
    },
    {
      "name": "Shenglong Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/61h3n7ft8x51k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20515",
  "fulltext_url": null,
  "id": "61h3n7ft8x51k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20515",
  "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": "W7221977109",
  "pdf_url": "https://arxiv.org/pdf/2610.20515",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/61h3n7ft8x51k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.20515",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20515"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction",
  "title_text": "Petz Recovery through a Single Polar Transformation for Approximate Quantum Error Correction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:31Z",
  "url": "https://research.draconitic.com/paper/61h3n7ft8x51k",
  "venue": "arXiv",
  "versions": []
}