{
  "abstract": "Predicting local fermionic correlations is a central task in quantum many-body physics, as these correlations encode many physically relevant local observables. The ubiquitous particle-number symmetry imposes strong structural constraints on quantum states, suggesting that local correlations should be learned with fewer samples than by symmetry-agnostic approaches. However, it has remained unclear whether such a provable advantage exists in collective learning of local correlations. Here, we develop a framework of number-conserving fermionic-shadow tomography based on random orbital rotations. We prove that, for every given order $k$, we can simultaneously estimate all $k$-body fermionic correlations of an $N$-mode $η$-particle state with a given variance $\\varepsilon^2$ using only $O_k(η^k/\\varepsilon^2)$ samples, which are independent of the system size $N$. We further establish a matching information-theoretic lower bound $Ω_k(η^k/\\varepsilon^2)$ for any adaptive protocol based on single-copy measurements, showing that the $(η^k,\\varepsilon)$-dependence is optimal up to constants depending only on $k$. Furthermore, numerical studies show a 20-fold query reduction for one-body correlation estimation at $N=200$, $η=20$, and $\\varepsilon=10^{-2}$, compared with the best alternative including Heisenberg-limited estimation methods. Relative to fermionic Gaussian-unitary shadows, sample costs for the square-lattice Fermi-Hubbard model at $N=288$ are reduced by factors of $148$ for energy density and $161$ for spin structure factor estimation. For molecular energy derivatives with respect to atomic coordinates, our method reduces sample requirements by factors of $53$ for $\\mathrm{Cr}_2$ and $18.5$ for $[\\mathrm{Fe}_2\\mathrm{S}_2]^{2-}$ at $N=128$. These results demonstrate the practical advantage of particle-number symmetry for fermionic observable estimation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.30601",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuki Koizumi"
    },
    {
      "name": "Kaito Wada"
    },
    {
      "name": "Toshinori P. Takama"
    },
    {
      "name": "Nobuyuki Yoshioka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/36ca2pyxrq9fj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.30601",
  "fulltext_url": null,
  "id": "36ca2pyxrq9fj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.30601",
  "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",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7166652699",
  "pdf_url": "https://arxiv.org/pdf/2606.30601",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/36ca2pyxrq9fj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2606.30601",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.30601"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Provably Efficient Learning of Fermionic Correlations under Particle-Number Symmetry",
  "title_text": "Provably Efficient Learning of Fermionic Correlations under Particle-Number Symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:48Z",
  "url": "https://research.draconitic.com/paper/36ca2pyxrq9fj",
  "venue": "arXiv",
  "versions": []
}