{
  "annotation_id": "99d592a5-40da-493e-be3c-27b568b5e714",
  "date_created": "2026-03-02T18:02:29.888000Z",
  "date_modified": "2026-03-02T18:02:29.888000Z",
  "file_hash": "1edad1119c13dd7d1c49dde9e42d4d5708627bba9d1aca1870294bca3d826d90",
  "private": false,
  "record": {
    "abstract": "We consider symmetric hypothesis testing in quantum statistics, where the\nhypotheses are density operators on a finite-dimensional complex Hilbert space,\nrepresenting states of a finite quantum system. We prove a lower bound on the\nasymptotic rate exponents of Bayesian error probabilities. The bound represents\na quantum extension of the Chernoff bound, which gives the best asymptotically\nachievable error exponent in classical discrimination between two probability\nmeasures on a finite set. In our framework, the classical result is reproduced\nif the two hypothetic density operators commute. Recently, it has been shown\nelsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is\nachievable also in the generic quantum (noncommutative) case. This implies that\nour result is one part of the definitive quantum Chernoff bound.",
    "arxiv_id": "quant-ph/0607216",
    "authors": [
      "Michael Nussbaum",
      "Arleta Szko\u0142a"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1214/08-AOS593",
    "journal_ref": "Annals of Statistics 2009, Vol. 37, No. 2, 1040-1057",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The Chernoff lower bound for symmetric quantum hypothesis testing",
    "url": "https://arxiv.org/abs/quant-ph/0607216"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6c4b653c-808d-4326-a5a8-1b7e26b12946",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}