{
  "annotation_id": "1416dd6f-796e-4d9a-98d8-e089ad6a6ef9",
  "date_created": "2026-03-02T18:02:31.028000Z",
  "date_modified": "2026-03-02T18:02:31.028000Z",
  "file_hash": "48c788a2bb179662ae4ec240f0cd43d56fc1de96068d4d586cc47906f50ca49d",
  "private": false,
  "record": {
    "abstract": "If the conditional information of a classical probability distribution of\nthree random variables is zero, then it obeys a Markov chain condition. If the\nconditional information is close to zero, then it is known that the distance\n(minimum relative entropy) of the distribution to the nearest Markov chain\ndistribution is precisely the conditional information. We prove here that this\nsimple situation does not obtain for quantum conditional information. We show\nthat for tri-partite quantum states the quantum conditional information is\nalways a lower bound for the minimum relative entropy distance to a quantum\nMarkov chain state, but the distance can be much greater; indeed the two\nquantities can be of different asymptotic order and may even differ by a\ndimensional factor.",
    "arxiv_id": "quant-ph/0611057",
    "authors": [
      "Ben Ibinson",
      "Noah Linden",
      "Andreas Winter"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-007-0362-8",
    "journal_ref": "Commun. Math. Phys. 277(2):289-304, 2008",
    "title": "Robustness of quantum Markov chains",
    "url": "https://arxiv.org/abs/quant-ph/0611057"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5fc86433-fa64-4e54-9f53-da5ddb302f70",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}