{
  "annotation_id": "5e4fbc4c-1882-4903-a2ab-09c54606e5a0",
  "date_created": "2026-03-02T18:02:45.031000Z",
  "date_modified": "2026-03-02T18:02:45.031000Z",
  "file_hash": "2e7f394809edb9a3d44855460574e33413128998c7ead1bb912a85e6c54692be",
  "private": false,
  "record": {
    "abstract": "We demonstrate --- using the case of the two-dimensional quantum systems ---\nthat the \"natural measure on the space of density matrices describing\nN-dimensional quantum systems\" proposed by Zyczkowski et al (quant-ph/9804024)\ndoes not belong to the class of normalized volume elements of monotone metrics\non the quantum systems. Such metrics possess the statistically important\nproperty of being decreasing under stochastic mappings (coarse-grainings). We\ndo note that the proposed natural measure (and certain evident variations upon\nit) exhibit quite specific monotonicity properties, but not of the form\nrequired for membership in the class.",
    "arxiv_id": "quant-ph/9904014",
    "authors": [
      "Paul B. Slater"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Lett. Math. Phys. 52: 343-348, 2000.",
    "title": "Monotonicity Properties of Certain Measures over the Two-Level Quantum   Systems",
    "url": "https://arxiv.org/abs/quant-ph/9904014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b7eb0d76-52de-45b4-94c8-bfddb9b9702b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}