{
  "abstract": "Fermionic non-Gaussianity is an essential resource for unlocking the full computational power of fermionic quantum platforms. In this work we develop monotones and efficient quantum algorithms for fermionic non-Gaussianity, all built on the eigenvalue structure of the operator $Λ= \\sum_{j=1}^{2n}γ_j\\otimesγ_j$ defined on two copies of an $n$-mode fermionic state, accessible via Bell sampling. In particular, we introduce the \\emph{bridge degree} of even pure states, a novel non-Gaussianity monotone defined as the largest eigenvalue of $Λ$ whose eigenspace is populated by two copies of the state. Our key technical result is that the bridge degree is non-increasing under post-selected Gaussian protocols, which yields no-go theorems for Gaussian conversion beyond the reach of previously known monotones and shows that the resource theory of fermionic non-Gaussianity is irreversible in the exact-conversion setting. Beyond this, the bridge degree exhibits several further features: it (i) is easy to compute, (ii) is efficiently witnessed through Bell sampling, (iii) lower-bounds the non-Gaussian gate complexity of state preparation, (iv) controls the non-Gaussian gate complexity of producing quantum state designs, and (v) naturally extends to mixed states via the Choi--Jamiołkowski isomorphism. We further develop an approximate variant together with an efficiently measurable lower bound, yielding an experimentally certifiable lower bound on the non-Gaussian cost of approximately preparing any state, based directly on Bell-sampling data. Finally, the same eigenvalue structure underlies two Bell-sampling-based algorithmic primitives, both with polynomial sample complexity: a two-copy Gaussianity test with perfect completeness, optimal among two-copy tests sharing this property, and a test for the state $2$-design property of matchgate-invariant ensembles.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: PRX Quantum 7, 033065 (2026)",
  "arxiv": "2606.05066",
  "author_total": 1,
  "authors": [
    {
      "name": "Poetri Sonya Tarabunga"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9yazffhvcmc93.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.05066",
  "fulltext_url": null,
  "id": "9yazffhvcmc93",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.05066",
  "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/2606.05066",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9yazffhvcmc93.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2606.05066",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.05066"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms",
  "title_text": "Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/9yazffhvcmc93",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/1bkz-7wf2",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}