{
  "abstract": "The no-cloning theorem is a cornerstone result in quantum mechanics that forbids copying of general quantum information. More quantitatively, even given $N$ copies of an unknown state, any channel producing an $(N+1)$-copy state incurs a nonzero trace-distance error on some inputs. Turning this around, one can ask about the sample complexity of approximate $N\\rightarrow N+1$ cloning: for a desired small error $ε$, what $N$ suffices? For arbitrary pure states on a Hilbert space $H$, the answer is $N\\simeq \\dim H/ε$ - astronomically large for most $H$ of interest. What if the input is promised to lie in a structured family? We examine a range of families fundamental to many-body physics and quantum information: $n$-mode fermionic Gaussian and Slater states, $n$-mode bosonic Gaussian states, and qudit phase states. For fermions, we construct optimal cloning channels, reducing the complexity from exponential to polynomial in $n$. For bosonic Gaussian states, we construct an explicit cloner that certifies polynomial complexity, without any constraint on the energy of the state; this channel, however, is not optimal in general. The fermionic and bosonic results follow from a single representation-theoretic framework, which generalizes previous work by Werner and by Chiribella and Yang; it also yields the cloners' unitary implementation. Furthermore, we explain why for many families the cloning complexity is linear in the dimension of the family manifold, via a controlled saddle-point evaluation of the frame potential at high $N$. The same calculation accounts for the analogous scaling of tomography complexity. The above framework does not cover phase states; for these we give an independent construction of a channel with optimal cloning fidelity. Our work complements recent results on cloning stabilizer states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06723",
  "author_total": 4,
  "authors": [
    {
      "name": "Yaroslav Herasymenko"
    },
    {
      "name": "Junqiao Lin"
    },
    {
      "name": "Philip Verduyn Lunel"
    },
    {
      "name": "Dmitry Grinko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3sjhh5sf87ems.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06723",
  "fulltext_url": null,
  "id": "3sjhh5sf87ems",
  "issns": [],
  "landing_url": "https://hal.science/hal-05783705v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.qphy"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7220648536",
  "pdf_url": "https://hal.science/hal-05783705/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3sjhh5sf87ems.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:50Z",
      "native_id": "hal-05783705",
      "source": "hal",
      "url": "https://hal.science/hal-05783705v1"
    },
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Approximate cloning of structured pure states",
  "title_text": "Approximate cloning of structured pure states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3sjhh5sf87ems",
  "venue": "HAL",
  "versions": []
}