{
  "annotation_id": "eb9613b5-7400-4d86-819c-214e4d926c9c",
  "date_created": "2026-03-02T18:02:47.656000Z",
  "date_modified": "2026-03-02T18:02:47.656000Z",
  "file_hash": "38d2f2c679cc57ffff60e59503686169010415a27e936b366a78b6f78a87630b",
  "private": false,
  "record": {
    "abstract": "It is the aim of this article to determine curvature quantities of an\narbitrary Riemannian monotone metric on the space of positive matrices resp.\nnonsingular density matrices. Special interest is focused on the scalar\ncurvature due to its expected quantum statistical meaning. The scalar curvature\nis explained in more detail for three examples, the Bures metric, the largest\nmonotone metric and the Kubo-Mori metric. In particular, we show an important\nconjecture of Petz concerning the Kubo-Mori metric up to a formal proof of the\nconcavity of a certain function on R_+^3. This concavity seems to be\nnumerically evident. The conjecture of Petz asserts that the scalar curvature\nof the Kubo-Mori metric increases if one goes to more mixed states.",
    "arxiv_id": "quant-ph/9906009",
    "authors": [
      "J. Dittmann"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "title": "On the Curvature of Monotone Metrics and a Conjecture Concerning the   Kubo-Mori Metric",
    "url": "https://arxiv.org/abs/quant-ph/9906009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "06c0d27c-d871-4afb-881a-aa0e3a815f11",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}