{
  "abstract": "A central yet mysterious problem in quantum information is the asymptotic distinguishability of quantum states under restricted measurements. Here we look at asymptotic asymmetric hypothesis testing for general multi-mode bosonic Gaussian states restricted to arbitrary collective Gaussian measurements. We establish a single-letter formula for the Stein exponent for many pairs of states, featuring two distinct contributions, corresponding to first and second moments, respectively. Remarkably, the Gaussian-measured relative entropy exhibits genuine non-additivity, but the only effect of additivity violations is to asymptotically decouple first and second moments. We prove this by establishing sufficient conditions for additivity of the second-moment term via novel log-determinant matrix inequalities. Our results not only identify a single-letter expression for the Gaussian Stein exponent in a wide range of practical situations, but also rule out any possible advantage from collective Gaussian measurements when considering centred Gaussian states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40307",
  "author_total": 5,
  "authors": [
    {
      "name": "Filippo Girardi"
    },
    {
      "name": "Jacopo Rizzo"
    },
    {
      "name": "Leah Turner"
    },
    {
      "name": "Gerardo Adesso"
    },
    {
      "name": "Ludovico Lami"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d00k5h6em2v6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40307",
  "fulltext_url": null,
  "id": "d00k5h6em2v6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40307",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7215115651",
  "pdf_url": "https://arxiv.org/pdf/2609.40307",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d00k5h6em2v6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40307",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40307"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A fully Gaussian quantum Stein's lemma",
  "title_text": "A fully Gaussian quantum Stein's lemma",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/d00k5h6em2v6q",
  "venue": "arXiv",
  "versions": []
}