{
  "annotation_id": "8cbbcf0b-9487-4d21-9faf-419a64e22bf5",
  "date_created": "2026-03-02T18:02:06.504000Z",
  "date_modified": "2026-03-02T18:02:06.504000Z",
  "file_hash": "fa3651b3f835d7be476d2da53bbc7f418c9ec63158ec51582213c42ad853ae74",
  "private": false,
  "record": {
    "abstract": "We derive the class of covariant measurements which are optimal according to\nthe maximum likelihood criterion. The optimization problem is fully resolved in\nthe case of pure input states, under the physically meaningful hypotheses of\nunimodularity of the covariance group and measurability of the stability\nsubgroup. The general result is applied to the case of covariant state\nestimation for finite dimension, and to the Weyl-Heisenberg displacement\nestimation in infinite dimension. We also consider estimation with multiple\ncopies, and compare collective measurements on identical copies with the scheme\nof independent measurements on each copy. A \"continuous-variables\" analogue of\nthe measurement of direction of the angular momentum with two anti-parallel\nspins by Gisin and Popescu is given.",
    "arxiv_id": "quant-ph/0403083",
    "authors": [
      "Giulio Chiribella",
      "Giacomo Mauro D\u0027Ariano",
      "Paolo Perinotti",
      "Massimiliano Federico Sacchi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.70.062105",
    "journal_ref": "Phys. Rev. A 70, 062105 (2004)",
    "title": "Covariant quantum measurements which maximize the likelihood",
    "url": "https://arxiv.org/abs/quant-ph/0403083"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "009d7be7-07f6-40f6-bbe0-88ddaa041061",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}