{
  "annotation_id": "04264d90-7046-41e3-b58f-9e6f58ec7790",
  "date_created": "2026-03-02T18:02:27.299000Z",
  "date_modified": "2026-03-02T18:02:27.299000Z",
  "file_hash": "ccb3e6896428ba161f9a9d1ea77fa679dbc8905b1b2945484ebc94e94f2c6bb9",
  "private": false,
  "record": {
    "abstract": "The generalized Pauli group and its normalizer, the Clifford group, have a\nrich mathematical structure which is relevant to the problem of constructing\nsymmetric informationally complete POVMs (SIC-POVMs). To date, almost every\nknown SIC-POVM fiducial vector is an eigenstate of a \"canonical\" unitary in the\nClifford group. I show that every canonical unitary in prime dimensions p \u003e 3\nlies in the same conjugacy class of the Clifford group and give a class\nrepresentative for all such dimensions. It follows that if even one such\nSIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them\nare (for a given such dimension). I also conjecture that in all dimensions d,\nthe number of conjugacy classes is bounded above by 3 and depends only on d mod\n9, and I support this claim with computer computations in all dimensions \u003c 48.",
    "arxiv_id": "quant-ph/0605050",
    "authors": [
      "Steven T. Flammia"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/39/43/007",
    "journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 13483-13493",
    "title": "On SIC-POVMs in Prime Dimensions",
    "url": "https://arxiv.org/abs/quant-ph/0605050"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1ec72b31-711d-46b6-b841-dc2b345a88f8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}