{
  "annotation_id": "fce14a44-5678-4f49-b78f-f2cf3a146f2b",
  "date_created": "2026-03-02T18:02:34.041000Z",
  "date_modified": "2026-03-02T18:02:34.041000Z",
  "file_hash": "5fd4da2c1c52a2302132e476b016cff11ce14f92040abdd6ab9a6c362286c202",
  "private": false,
  "record": {
    "abstract": "This paper deals with bases in a finite-dimensional Hilbert space. Such a\nspace can be realized as a subspace of the representation space of SU(2)\ncorresponding to an irreducible representation of SU(2). The representation\ntheory of SU(2) is reconsidered via the use of two truncated deformed\noscillators. This leads to replace the familiar scheme {j^2, j_z} by a scheme\n{j^2, v(ra)}, where the two-parameter operator v(ra) is defined in the\nenveloping algebra of the Lie algebra su(2). The eigenvectors of the commuting\nset of operators {j^2, v(ra)} are adapted to a tower of chains SO(3) \u003e C(2j+1),\n2j integer, where C(2j+1) is the cyclic group of order 2j+1. In the case where\n2j+1 is prime, the corresponding eigenvectors generate a complete set of\nmutually unbiased bases. Some useful relations on generalized quadratic Gauss\nsums are exposed in three appendices.",
    "arxiv_id": "quant-ph/0701230",
    "authors": [
      "O. Albouy",
      "M. R. Kibler"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "journal_ref": "SIGMA (Symmetry, Integrability and Geometry: Methods and\n  Applications) 3 (2007) 076",
    "title": "SU(2) nonstandard bases: the case of mutually unbiased bases",
    "url": "https://arxiv.org/abs/quant-ph/0701230"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7801f391-39f9-4fb9-8186-9e60056e5d8a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}