{
  "abstract": "We determine asymptotic global fidelities of cloning generic mixed states with simple (non-degenerate) full-rank spectra. In fixed dimension $d$, let $n$ inputs and $m_n$ outputs satisfy $m_n/n\\toγ>1$. For a known simple full-rank spectrum $p_1>\\cdots>p_d>0$, we prove that the optimal root fidelity between the entire output and the product target state is $$ F_\\rm{orb}(γ,p) =\\prod_{i<j} \\frac{\\sqrtγ+\\sqrt{q_{ij}(γ-1+q_{ij})}} {γ+q_{ij}}, \\qquad q_{ij}=\\frac{p_j}{p_i}. $$ When the spectrum is unknown, one spectrum-independent cloner attains $$ F_\\rm{univ}(γ,p) =\\left(\\frac{2\\sqrtγ}{1+γ}\\right)^{(d-1)/2} F_\\rm{orb}(γ,p), $$ uniformly on compact subsets of the simple full-rank chamber and is minimax optimal. The two factors quantify spectral and eigenbasis uncertainty. Our channels combine classical processing of Schur--Weyl labels with a covariant Cartan-sector channel. Local asymptotic normality and a Gaussian fidelity bound against arbitrary channels yield the converses. For flat projector states $ρ=P/r$, with $P$ a rank-$r$ orthogonal projector, we separately prove the optimum $γ^{-r(d-r)/2}$. Furthermore, we estimate the exact asymptotic fidelity of purify--clone--trace (PCT), and show that our cloners strictly outperform PCT at every fixed gain for simple full-rank spectra and rank-$r$ projector states with $1<r<d$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35986",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiani Fei"
    },
    {
      "name": "Jinzhao Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2xznnhfkyh2y3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35986",
  "fulltext_url": null,
  "id": "2xznnhfkyh2y3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35986",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214919594",
  "pdf_url": "https://arxiv.org/pdf/2609.35986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xznnhfkyh2y3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.35986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Asymptotically Optimal Mixed-State Cloning",
  "title_text": "Asymptotically Optimal Mixed-State Cloning",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/2xznnhfkyh2y3",
  "venue": "arXiv",
  "versions": []
}