{
  "annotation_id": "a014bd1c-aff2-4801-abe5-ab1c08c21bd9",
  "date_created": "2026-03-02T18:02:00.221000Z",
  "date_modified": "2026-03-02T18:02:00.221000Z",
  "file_hash": "23f46ec67059af551fe4a7454b3d93bc7d88fb3175942f8cf1bf73e105e10dd8",
  "private": false,
  "record": {
    "abstract": "We give an explicit characterisation of the quantum states which saturate the\nstrong subadditivity inequality for the von Neumann entropy. By combining a\nresult of Petz characterising the equality case for the monotonicity of\nrelative entropy with a recent theorem by Koashi and Imoto, we show that such\nstates will have the form of a so-called short quantum Markov chain, which in\nturn implies that two of the systems are independent conditioned on the third,\nin a physically meaningful sense. This characterisation simultaneously\ngeneralises known necessary and sufficient entropic conditions for quantum\nerror correction as well as the conditions for the achievability of the Holevo\nbound on accessible information.",
    "arxiv_id": "quant-ph/0304007",
    "authors": [
      "Patrick Hayden",
      "Richard Jozsa",
      "Denes Petz",
      "Andreas Winter"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-004-1049-z",
    "journal_ref": "Commun. Math. Phys., 246(2):359-374, 2004",
    "title": "Structure of states which satisfy strong subadditivity of quantum   entropy with equality",
    "url": "https://arxiv.org/abs/quant-ph/0304007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8be84e80-d7b1-4ae1-bce6-1a11c705ad69",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}