{
  "abstract": "Free-fermion states are classically simulable, yet, written as qubits, they typically carry extensive magic, the quantum resource that stabilizer circuits lack. Part of this magic is nonlocal: local unitaries acting separately on two parts of the system cannot remove it. If these local unitaries are restricted to Gaussian ones, the nonlocal magic grows linearly with the number $m$ of partially entangled fermion pairs. We show that this growth is an artifact of the Gaussian restriction: local Gaussian unitaries minimize the nonlocal stabilizer Rényi entropy for up to three pairs, but not from four pairs on. General local non-Gaussian unitaries that respect fermion parity take $m$ free-fermion pairs to fermionic Bell pairs with a fidelity that decays at most as $1/\\sqrt m$ compared to exponential decay with Gaussian unitaries, so the nonlocal magic drops from linear to logarithmic in $m$. The reason is statistical --- Bell pairs have equal Schmidt weights, that is, a fully degenerate entanglement spectrum, and a state can stay far from them only if its Schmidt weights are spread over many orders of magnitude. This spread is measured by the capacity of entanglement $C_E$, the variance of the entanglement Hamiltonian, and the nonlocal magic of any fermionic state grows at most logarithmically with $C_E$. Free-fermion pairs add to $C_E$ independently, so $C_E$ grows only linearly in $m$, and this leads to the stabilizer fidelity decreasing at most as $1/\\sqrt m$. Almost all the magic of free fermions, including Hartree--Fock and BCS mean-field states, is therefore local.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07003",
  "author_total": 4,
  "authors": [
    {
      "name": "Raghav G. Jha"
    },
    {
      "name": "Dengyao Luo"
    },
    {
      "name": "Alexander F. Kemper"
    },
    {
      "name": "Bojko N. Bakalov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/13k10ve14g37q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07003",
  "fulltext_url": null,
  "id": "13k10ve14g37q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07003",
  "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.other"
    ],
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07003",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/13k10ve14g37q.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.07003",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07003"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.other",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Nonlocal magic of fermions is bounded by entanglement fluctuations and is logarithmic for free fermions",
  "title_text": "Nonlocal magic of fermions is bounded by entanglement fluctuations and is logarithmic for free fermions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:39Z",
  "url": "https://research.draconitic.com/paper/13k10ve14g37q",
  "venue": "arXiv",
  "versions": []
}