{
  "abstract": "Chen, Mele, Mele and Preskill proved a crossover for bosonic Gaussian tomography: cold states need $Θ(m^3/ε^2)$ copies under single-copy or few-copy measurements, warm ones $Θ(m^2/ε^2)$. The author proved $Ω(m^3/ε^2)$ for adaptive single-copy tomography of mixed fermionic Gaussian states. This note shows the crossover has no fermionic counterpart and extends the fermionic bound to blocks of $k$ copies. There is no warm regime: on the quadratic Gibbs balls $β\\|h\\|_F\\leβ_0$ of unknown Hamiltonian $h$, the single-copy rate is $Θ(m^3/ε^2)$ for every fixed $β_0>0$, at accuracies that resolve the ball, with a lower-bound constant independent of $β_0$. At the maximally mixed state a replicated-parameter Fisher budget gives $N>m^3/(8{,}553{,}600\\,k\\,ε^2)$ for blocks of at most $k$ copies and all $ε\\le1/3600$; an exact formula for the maximal block Fisher information, via spinor tensor powers of $\\mathfrak{so}(2m)$, shows that the budget $mt^2$ behind it is asymptotically attained for every fixed block size; whether $1/k$ is the true rate is open. Near the vacuum, block protocols need $Ω(m^3/(ε^2\\min\\{\\sqrt k,m\\}))$ copies, with no logarithm, via an exterior-power embedding of qudit tomography; parity superselection changes no rate, and number superselection costs nothing on number-conserving inputs. The embedding also carries upper bounds: a particle-number measurement followed by the $k$-copy qudit protocol of Nayak and Zhou attains the lower bound for every $k$ on number-conserving fermionic Gaussian states with bounded fugacity trace and on passive bosonic Gaussian states with bounded photon number, and a heterodyne stage that undoes displacement and squeezing extends this to all cold bosonic Gaussian states. This closes their $k$-entangled gap on the cold class; intermediate temperatures remain open.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07271",
  "author_total": 1,
  "authors": [
    {
      "name": "Ron Rubin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agr75ch2vygbv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07271",
  "fulltext_url": null,
  "id": "agr75ch2vygbv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07271",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agr75ch2vygbv.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07271"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Upper and lower bounds for few-copy Gaussian tomography, and the absence of a fermionic warm regime",
  "title_text": "Upper and lower bounds for few-copy Gaussian tomography, and the absence of a fermionic warm regime",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:40Z",
  "url": "https://research.draconitic.com/paper/agr75ch2vygbv",
  "venue": "arXiv",
  "versions": []
}