{
  "abstract": "For centered bosonic Gaussian states, the covariance pullback of the Bures cometric differs from the lift-normalized classical covariance Fisher--Rao cometric by a state-independent bilinear form. Under the canonical identification of symmetric covariance covectors with $\\mathfrak{sp}(2N,\\mathbb{R})$, this form is the trace form and hence a fixed multiple of the Killing form. We prove that, within the normalized symmetric Petz family, Bures is uniquely selected by requiring such an additive state-independent symplectic correction. We determine the full Williamson-frame spectrum and show that a boundary stratum with $m$ pure modes has an $m^2$-dimensional cometric kernel isomorphic to $\\mathfrak u(m)$, while the pure Gaussian orbit remains nondegenerate. For radial one-mode estimation, ideal heterodyne detection accesses the exact fraction $(ν-\\hbar/2)/(ν+\\hbar/2)$ of the SLD quantum Fisher information. Its vanishing boundary limit reflects finite heterodyne information relative to a divergent radial quantum Fisher information, not zero measurement information. Finally, a minimal Schur realization fixes the auxiliary inertia and identifies the second Schur complement as the true covariant vertical block.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16376",
  "author_total": 1,
  "authors": [
    {
      "name": "Christian Kerskens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4386e92t1nh7m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16376",
  "fulltext_url": null,
  "id": "4386e92t1nh7m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16376",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7169858804",
  "pdf_url": "https://arxiv.org/pdf/2607.16376",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4386e92t1nh7m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2607.16376",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16376"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Killing Form and Petz Uniqueness of Gaussian Bures Geometry",
  "title_text": "The Killing Form and Petz Uniqueness of Gaussian Bures Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/4386e92t1nh7m",
  "venue": "arXiv",
  "versions": []
}