{
  "annotation_id": "16e535cc-26a4-4e3d-8ca9-37684aeb0d75",
  "date_created": "2026-03-02T18:01:42.079000Z",
  "date_modified": "2026-03-02T18:01:42.079000Z",
  "file_hash": "d99381c7170cc66764fa31e83a1345fa7b0c8c4b580595785cfd41e8b3dcecdd",
  "private": false,
  "record": {
    "abstract": "Chentsov studied Riemannian metrics on the set of probability measures from\nthe point of view of decision theory. He proved that up to a constant factor\nthe Fisher information is the only metric which is monotone under stochastic\ntransformations. The present paper deals with monotone metrics on the space of\nfinite density matrices on the basis motivated by quantum mechanics. A\ncharacterization of those metrics is given in terms of operator monotone\nfunctions. Several concrete metrics are constructed and analyzed, in\nparticular, instead of the uniqueness in the probabilistic case, there is a\nlarge class of monotone metrics. Some of those appeared already in the physics\nliterature a long time ago. A limiting procedure to pure states is discussed as\nwell.",
    "arxiv_id": "quant-ph/0102132",
    "authors": [
      "D. Petz",
      "Cs. Sudar"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "in \"Geometry in Present Days Science\", eds. O.E. Barndorff-Nielsen\n  and E.B. Vendel Jensen, World Scientific 1999, pp. 21-34",
    "title": "Extending the Fisher metric to density matrices",
    "url": "https://arxiv.org/abs/quant-ph/0102132"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "25e7fc0a-44c2-4be6-a336-38ae19cac7c2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}