{
  "annotation_id": "8b058631-46a0-415d-99fa-f6b5429192dc",
  "date_created": "2026-03-02T18:02:45.137000Z",
  "date_modified": "2026-03-02T18:02:45.137000Z",
  "file_hash": "6e9c7ef22d7221276c578826564de5154dab6285896103041863b94543791970",
  "private": false,
  "record": {
    "abstract": "The Riemannian Bures metric on the space of (normalized) complex positive\nmatrices is used for parameter estimation of mixed quantum states based on\nrepeated measurements just as the Fisher information in classical statistics.\nIt appears also in the concept of purifications of mixed states in quantum\nphysics. Here we determine its scalar curvature and Ricci tensor and prove a\nlower bound for the curvature on the submanifold of trace one matrices. This\nbound is achieved for the maximally mixed state, a further hint for the quantum\nstatistical meaning of the scalar curvature.",
    "arxiv_id": "quant-ph/9810012",
    "authors": [
      "J. Dittmann"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.DG",
      "math.MP"
    ],
    "doi": "10.1016/S0393-0440(98)00068-0",
    "journal_ref": "J.Geom.Phys. 31 (1999) 16-24",
    "title": "The Scalar Curvature of the Bures Metric on the Space of Density   Matrices",
    "url": "https://arxiv.org/abs/quant-ph/9810012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "876956af-f7b9-4b3e-bb21-1da31a6ef426",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}