{
  "annotation_id": "16c859c8-8886-42d9-aa21-26646f0ce295",
  "date_created": "2026-03-02T18:01:45.894000Z",
  "date_modified": "2026-03-02T18:01:45.894000Z",
  "file_hash": "38e6927c803c5dc5fa1b9854ae43d68a31048315f771c32923e63b54eb7c3ba1",
  "private": false,
  "record": {
    "abstract": "We study the mathematical structure of covariant phase observables. Such an\nobservable can alternatively be expressed as a phase matrix, as a sequence of\nunit vectors, as a sequence of phase states, or as an equivalent class of\ncovariant trace-preserving operations. Covariant generalized operator measures\nare defined by structure matrices which form a W*-algebra with phase matrices\nas its subset. The properties of the Radon-Nikodym derivatives of phase\nprobability measures are studied.",
    "arxiv_id": "quant-ph/0108105",
    "authors": [
      "Juha-Pekka Pellonpaa"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1446663",
    "journal_ref": "J. Math. Phys. 43 (2002) 1299-1308",
    "title": "On the structure of covariant phase observables",
    "url": "https://arxiv.org/abs/quant-ph/0108105"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "146d869a-9f19-432b-9bc1-1734707a66e7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}