{
  "annotation_id": "bcf0e7f1-a6ad-4c35-8776-0055478c459d",
  "date_created": "2026-03-02T18:02:40.780000Z",
  "date_modified": "2026-03-02T18:02:40.780000Z",
  "file_hash": "e3864d6508ee56a32582fefb2ec82d45c7f5eb0cbc9c047c60a8d40dffcc0db5",
  "private": false,
  "record": {
    "abstract": "To calculate the entropy of a subalgebra or of a channel with respect to a\nstate, one has to solve an intriguing optimalization problem. The latter is\nalso the key part in the entanglement of formation concept, in which case the\nsubalgebra is a subfactor. I consider some general properties, valid for these\ndefinitions in finite dimensions, and apply them to a maximal commutative\nsubalgebra of a full matrix algebra. The main method is an interplay between\nconvexity and symmetry. A collection of helpful tools from convex analysis for\nthe problems in question is collected in an appendix.",
    "arxiv_id": "quant-ph/9704017",
    "authors": [
      "Armin Uhlmann"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Entropy and optimal decompositions of states relative to a maximal   commutative subalgebra",
    "url": "https://arxiv.org/abs/quant-ph/9704017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c9987dcf-a503-42e3-95c0-1aeac95914f6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}