{
  "abstract": "Deciding whether an unknown quantum state either belongs to, or is far from, a given family of states is a natural question of quantum information theory. In many such cases, there is a natural 2-copy test which always accepts whenever the state indeed belongs to the target family; it is often much more difficult, however, to bound the probability of acceptance for states that are far from the family. Here we develop a simple new technique for upper bounding this probability for general families, and therefore upper bounding the sample-complexity of the decision problem itself. As a particularly striking example of this framework, we show that deciding whether an unknown pure $n$-mode state is fermionic Gaussian, or at least $\\varepsilon$-far in trace distance from all Gaussian states, can be accomplished using the optimal number $Θ(\\varepsilon^{-2})$ of copies. Remarkably, our analysis applies to the well-known Bell sampling procedure for testing fermionic Gaussianity, which we therefore show to be optimal, even compared to protocols making arbitrary collective and adaptive measurements. As a second example, we show that the analogous decision problem for the family of Slater determinant states can also be solved with mode-independent sample-complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02050",
  "author_total": 2,
  "authors": [
    {
      "name": "Maxwell West"
    },
    {
      "name": "Martin Larocca"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b0sncyymjvjqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02050",
  "fulltext_url": null,
  "id": "b0sncyymjvjqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02050",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7216365744",
  "pdf_url": "https://arxiv.org/pdf/2610.02050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b0sncyymjvjqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02050"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Fermionic Gaussianity can be tested with mode-independent sample-complexity",
  "title_text": "Fermionic Gaussianity can be tested with mode-independent sample-complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/b0sncyymjvjqr",
  "venue": "arXiv",
  "versions": []
}