{
  "annotation_id": "dec88775-6cd2-4f1f-b561-edd13d3837d1",
  "date_created": "2026-03-02T18:02:09.944000Z",
  "date_modified": "2026-03-02T18:02:09.944000Z",
  "file_hash": "fd2f4cd9febffb4d973344059bb32a3f137b16cf08fc6ea27f208c54f05f3d34",
  "private": false,
  "record": {
    "abstract": "A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of\ndimension d, whenever d is a power of a prime. We discuss a simple construction\nof d+1 disjoint classes (each one having d-1 commuting operators) such that the\ncorresponding eigenstates form sets of unbiased bases. Such a construction\nworks properly for prime dimension. We investigate an alternative construction\nin which the real numbers that label the classes are replaced by a finite field\nhaving d elements. One of these classes is diagonal, and can be mapped to\ncyclic operators by means of the finite Fourier transform, which allows one to\nunderstand complementarity in a similar way as for the position-momentum pair\nin standard quantum mechanics. The relevant examples of two and three qubits\nand two qutrits are discussed in detail.",
    "arxiv_id": "quant-ph/0410155",
    "authors": [
      "A. B. Klimov",
      "L. L. Sanchez-Soto",
      "H. de Guise"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/38/12/015",
    "journal_ref": "Journal of Physics A 38, 2747--2760 (2005)",
    "title": "Multicomplementary operators via finite Fourier transform",
    "url": "https://arxiv.org/abs/quant-ph/0410155"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "24462e7c-ee9c-42b6-87e1-49c0de0ab57f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}