{
  "annotation_id": "d8394a6e-6c4f-454a-a790-e0a688ec1996",
  "date_created": "2026-03-02T18:02:06.940000Z",
  "date_modified": "2026-03-02T18:02:06.940000Z",
  "file_hash": "8d49cdb91c4676c26bac956fa268438f06845719eb07ab6ab534f5c797f84bf3",
  "private": false,
  "record": {
    "abstract": "The original Wigner function provides a way of representing in phase space\nthe quantum states of systems with continuous degrees of freedom. Wigner\nfunctions have also been developed for discrete quantum systems, one popular\nversion being defined on a 2N x 2N discrete phase space for a system with N\northogonal states. Here we investigate an alternative class of discrete Wigner\nfunctions, in which the field of real numbers that labels the axes of\ncontinuous phase space is replaced by a finite field having N elements. There\nexists such a field if and only if N is a power of a prime; so our formulation\ncan be applied directly only to systems for which the state-space dimension\ntakes such a value. Though this condition may seem limiting, we note that any\nquantum computer based on qubits meets the condition and can thus be\naccommodated within our scheme. The geometry of our N x N phase space also\nleads naturally to a method of constructing a complete set of N+1 mutually\nunbiased bases for the state space.",
    "arxiv_id": "quant-ph/0401155",
    "authors": [
      "Kathleen S. Gibbons",
      "Matthew J. Hoffman",
      "William K. Wootters"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.70.062101",
    "journal_ref": "Phys. Rev. A 70, 062101 (2004)",
    "title": "Discrete phase space based on finite fields",
    "url": "https://arxiv.org/abs/quant-ph/0401155"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b834b18a-5fb8-45a9-a99f-db1140836b61",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}