{
  "abstract": "Quantum purity amplification (QPA) is the task of coherently transforming $n$ copies of a mixed state into high-fidelity copies of a chosen eigenstate. We develop a general theory of QPA for $n$ input copies, $m$ output copies, and arbitrary choices of target eigenstate, local dimension $d$, and input spectrum. We introduce the overhang-removal protocol, derive its all-site and one-site fidelities across output regimes, and show that it is optimal in several regimes, both asymptotically and nonasymptotically. For the asymptotic analysis, we use a path-graph parametrization to show that, when the target eigenvalue has a constant spectral gap $D_{k,\\mathrm{min}}$, achieving worst-case all-site error $\\varepsilon$ scales as $O(m/(\\varepsilon D_{k,\\mathrm{min}}^2))$. When $m/n$ approaches a constant, the performance exhibits phase-like regimes, which we characterize explicitly. For the nonasymptotic analysis, we develop a theory of generalized Young diagrams that yields tight sample complexity bounds and provides the first tight dimension-uniform guarantee for optimal QPA. We also provide asymptotically efficient implementations of the overhang-removal protocol. Together, these results establish QPA as a rigorous example of coherent quantum information processing with dimension-uniform sample complexity, supplying the technical foundation for the coherent-incoherent separation developed in the companion work.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.21570",
  "author_total": 4,
  "authors": [
    {
      "name": "Zhaoyi Li"
    },
    {
      "name": "Elias Theil"
    },
    {
      "name": "Aram W. Harrow"
    },
    {
      "name": "Isaac Chuang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4h44vj4w092t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.21570",
  "fulltext_url": null,
  "id": "f4h44vj4w092t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.21570",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7162118427",
  "pdf_url": "https://arxiv.org/pdf/2605.21570",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4h44vj4w092t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2605.21570",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.21570"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs",
  "title_text": "Quantum Purity Amplification for Arbitrary Eigenstates and Multiple Outputs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/f4h44vj4w092t",
  "venue": "arXiv",
  "versions": []
}