{
  "annotation_id": "07c4792c-8792-4b1d-851f-ad963c5db439",
  "date_created": "2026-03-02T18:02:22.884000Z",
  "date_modified": "2026-03-02T18:02:22.884000Z",
  "file_hash": "b1236b1140a0df793935c488d7e0924d911356fca5bd9df1bf5a12f46a3f2cfe",
  "private": false,
  "record": {
    "abstract": "The relative entropy of two n-party quantum states is an important quantity\nexhibiting, for example, the extent to which the two states are different. The\nrelative entropy of the states formed by reducing two n-party to a smaller\nnumber $m$ of parties is always less than or equal to the relative entropy of\nthe two original n-party states. This is the monotonicity of relative entropy.\n  Using techniques from convex geometry, we prove that monotonicity under\nrestrictions is the only general inequality satisfied by relative entropies. In\ndoing so we make a connection to secret sharing schemes with general access\nstructures.\n  A suprising outcome is that the structure of allowed relative entropy values\nof subsets of multiparty states is much simpler than the structure of allowed\nentropy values. And the structure of allowed relative entropy values (unlike\nthat of entropies) is the same for classical probability distributions and\nquantum states.",
    "arxiv_id": "quant-ph/0511260",
    "authors": [
      "Ben Ibinson",
      "Noah Linden",
      "Andreas Winter"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-006-0081-6",
    "journal_ref": "Commun. Math. Phys. 269(1):223-238, 2007",
    "title": "All Inequalities for the Relative Entropy",
    "url": "https://arxiv.org/abs/quant-ph/0511260"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ac46f5a8-b593-47de-8cf1-eb896fdfcdb4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}