{
  "annotation_id": "e24733d4-3c17-413e-99bc-8cf63c8759d8",
  "date_created": "2026-03-02T18:02:16.354000Z",
  "date_modified": "2026-03-02T18:02:16.354000Z",
  "file_hash": "7867fdeb6e73b3632de77456fb7e6cf3236b9b006456d2503da7486773603e24",
  "private": false,
  "record": {
    "abstract": "The quantum relative entropy is frequently used as a distance, or\ndistinguishability measure between two quantum states. In this paper we study\nthe relation between this measure and a number of other measures used for that\npurpose, including the trace norm distance. More precisely, we derive lower and\nupper bounds on the relative entropy in terms of various distance measures for\nthe difference of the states based on unitarily invariant norms. The upper\nbounds can be considered as statements of continuity of the relative entropy\ndistance in the sense of Fannes. We employ methods from optimisation theory to\nobtain bounds that are as sharp as possible.",
    "arxiv_id": "quant-ph/0503218",
    "authors": [
      "K. M. R. Audenaert",
      "J. Eisert"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.2044667",
    "journal_ref": "J. Math. Phys. 46, 102104 (2005)",
    "title": "Continuity bounds on the quantum relative entropy",
    "url": "https://arxiv.org/abs/quant-ph/0503218"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "894340c2-4cb5-49b0-aa45-98b54ba35720",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}