{
  "annotation_id": "1e9d04fe-1b7f-4503-815c-3b536f38144e",
  "date_created": "2026-03-02T18:01:45.957000Z",
  "date_modified": "2026-03-02T18:01:45.957000Z",
  "file_hash": "e1f3faed3ab6ec48f348d2c1f466bdf9ed6ef94a0eaeaaf1a85245b058cbde4c",
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  "record": {
    "abstract": "We explore and develop the mathematics of the theory of entanglement\nmeasures. After a careful review and analysis of definitions, of preliminary\nresults, and of connections between conditions on entanglement measures, we\nprove a sharpened version of a uniqueness theorem which gives necessary and\nsufficient conditions for an entanglement measure to coincide with the reduced\nvon Neumann entropy on pure states. We also prove several versions of a theorem\non extreme entanglement measures in the case of mixed states. We analyse\nproperties of the asymptotic regularization of entanglement measures proving,\nfor example, convexity for the entanglement cost and for the regularized\nrelative entropy of entanglement.",
    "arxiv_id": "quant-ph/0105017",
    "authors": [
      "Matthew J. Donald",
      "Michal Horodecki",
      "Oliver Rudolph"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.1495917",
    "journal_ref": "J. Math. Phys. 43 (2002) 4252-4272",
    "title": "The Uniqueness Theorem for Entanglement Measures",
    "url": "https://arxiv.org/abs/quant-ph/0105017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "812c1196-4137-4d63-a04b-eb332cc2ffea",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}