{
  "abstract": "We characterize the magic of random fermionic Gaussian states through their Pauli spectrum and their stabilizer entropies. For the Haar ensemble of Majorana Gaussian states we derive closed finite-$N$ expressions for the average stabilizer purities and reconstruct the Pauli spectrum exactly, as a mixture of products of beta-distributed variables resolved by Majorana weight. The stabilizer entropies, and their filtered versions, freeze at Rényi index $q_c=2$: for $q>2$ the magic density is $1/(q-1)$, controlled by rare weight-two Majorana strings. Resolving these contributions requires exponentially many characteristic samples, making direct sampling estimates of the stabilizer entropies inefficient in this frozen regime. For Haar-random Gaussian states at fixed filling, we express the averaged stabilizer purities at positive integer $q$ as coefficient integrals over $\\mathrm{SU}(2q)$, with dimension independent of $N$, and evaluate the $q=2$ case exactly. We establish that the frozen density describes typical states in the Majorana and half-filled number-conserving ensembles and relate these ensembles to the corresponding $\\mathrm{SYK}_2$ ground states. Finally, we show that typical fermionic Gaussian states retain certified magic after discarding any fixed fraction $κ<κ_\\star^{\\rm G}\\simeq0.7613$ of their modes in the thermodynamic limit, remaining magical even beyond the $2/3$ threshold for Haar-random states in the full Hilbert space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15739",
  "author_total": 3,
  "authors": [
    {
      "name": "Xhek Turkeshi"
    },
    {
      "name": "Piotr Sierant"
    },
    {
      "name": "Poetri Sonya Tarabunga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7w1pp88rfra9r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15739",
  "fulltext_url": null,
  "id": "7w1pp88rfra9r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15739",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213333165",
  "pdf_url": "https://arxiv.org/pdf/2609.15739",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7w1pp88rfra9r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15739",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15739"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Pauli spectrum and nonstabilizerness of random fermionic Gaussian states",
  "title_text": "Pauli spectrum and nonstabilizerness of random fermionic Gaussian states",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/7w1pp88rfra9r",
  "venue": "arXiv",
  "versions": []
}