{
  "annotation_id": "be576af9-2e27-404d-a6e0-9b82a009b847",
  "date_created": "2026-03-02T18:02:03.424000Z",
  "date_modified": "2026-03-02T18:02:03.424000Z",
  "file_hash": "7750a72ee9cbc37f426574b9e129b35c5b4d90a3ae68ffe9a0fad6134bf7620e",
  "private": false,
  "record": {
    "abstract": "Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K).\nAssume that density matrices D_1 and D_2 acting on H are given. In the paper\nthe consequences of the existence of a coarse-graining S from B(K) to B(H)\nsatisfying ST(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the\nsufficiency of T for D_1 and D_2.) Sufficiency implies a particular\ndecomposition of the density matrices. This decomposition allows to deduce the\nexact condition for equality in the strong subadditivity of the von Neumann\nentropy.",
    "arxiv_id": "quant-ph/0312221",
    "authors": [
      "Milan Mosonyi",
      "Denes Petz"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s11005-004-4072-2",
    "journal_ref": "Lett. Math. Phys. 68(2004), 19-30.",
    "title": "Structure of sufficient quantum coarse-grainings",
    "url": "https://arxiv.org/abs/quant-ph/0312221"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a848d54b-e5b3-4cff-9d35-d34cafb5b6de",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}