{
  "annotation_id": "7cfba04a-b14c-4f01-ab4c-9e298a564775",
  "date_created": "2026-03-02T18:02:13.627000Z",
  "date_modified": "2026-03-02T18:02:13.627000Z",
  "file_hash": "33fec0bbe3ee5ea85c8019bdeb057afaa7e48554611a95673f54f226a10b79d4",
  "private": false,
  "record": {
    "abstract": "We show that for a convex function the following, rather modest conditions,\nare equivalent to monotonicity under local operations and classical\ncommunication. The conditions are: 1)invariance under local unitaries, 2)\ninvariance under adding local ancilla in arbitrary state 3) on mixtures of\nstates possessing local orthogonal flags the function is equal to its average.\nThe result holds for multipartite systems. It is intriguing that the obtained\nconditions are equalities. The only inequality is hidden in the condition of\nconvexity.",
    "arxiv_id": "quant-ph/0412210",
    "authors": [
      "Michal Horodecki"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Open Syst. Inf. Dyn. 12, 231 (2005)",
    "title": "Simplifying monotonicity conditions for entanglement measures",
    "url": "https://arxiv.org/abs/quant-ph/0412210"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4309b557-4e04-4143-8ad6-01da73af4915",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}