{
  "abstract": "We prove a separability rigidity theorem for finite-mode Gaussian states. Let $ρ_G$ be Gaussian and let $\\mathcal I$ be a fixed partition of the modes. If $ρ_G$ dominates a nonzero positive operator $T$ that is separable across $\\mathcal I$, $0\\neq T\\preccurlyeq ρ_G$, then $ρ_G$ itself is separable across $\\mathcal I$. The dominated operator is arbitrary and need not be Gaussian. The theorem has three applications. First, any Gaussian channel admitting a nonzero entanglement-breaking completely positive subchannel is itself entanglement breaking, even when that subchannel is non-Gaussian. Second, if a resource state dominates a positive multiple of a faithful separable state, no finite-copy, postselected separability-preserving protocol can prepare an entangled Gaussian state exactly with nonzero success probability. Third, a connected graph of entangled Gaussian two-mode marginals certifies genuine multipartite entanglement of every compatible global state, even if the global state is non-Gaussian; the certification is robust to sufficiently small trace-norm errors in the marginals. As a structural corollary, mixing states separable across different partitions cannot produce new Gaussian states, so full inseparability and genuine multipartite entanglement coincide for finite-mode Gaussian states and identical copies of a biseparable Gaussian state cannot activate genuine multipartite entanglement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36336",
  "author_total": 2,
  "authors": [
    {
      "name": "Evgeny Shchukin"
    },
    {
      "name": "Peter van Loock"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s3hzxyf4fgq0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36336",
  "fulltext_url": null,
  "id": "2s3hzxyf4fgq0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36336",
  "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": "W7214904763",
  "pdf_url": "https://arxiv.org/pdf/2609.36336",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s3hzxyf4fgq0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2609.36336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36336"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Separability rigidity of Gaussian states under positive domination",
  "title_text": "Separability rigidity of Gaussian states under positive domination",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:50Z",
  "url": "https://research.draconitic.com/paper/2s3hzxyf4fgq0",
  "venue": "arXiv",
  "versions": []
}