{
  "annotation_id": "798d3d13-bd67-4776-8083-4da44f2e9daf",
  "date_created": "2026-03-02T18:02:10.339000Z",
  "date_modified": "2026-03-02T18:02:10.339000Z",
  "file_hash": "15ace7c7ffd52433e3c1414d73f420112bd283cea8df7e8e131e1dd3319b5580",
  "private": false,
  "record": {
    "abstract": "We develop a comprehensive theory of phase for finite-dimensional quantum\nsystems. The only physical requirement we impose is that phase is complementary\nto amplitude. To implement this complementarity we use the notion of mutually\nunbiased bases, which exist for dimensions that are powers of a prime. For a\nd-dimensional system (qudit) we explicitly construct d+1 classes of maximally\ncommuting operators, each one consisting of d-1 operators. One of this class\nconsists of diagonal operators that represent amplitudes (or inversions). By\nthe finite Fourier transform, it is mapped onto ladder operators that can be\nappropriately interpreted as phase variables. We discuss the examples of qubits\nand qutrits, and show how these results generalize previous approaches.",
    "arxiv_id": "quant-ph/0410135",
    "authors": [
      "A. B. Klimov",
      "L. L. Sanchez-Soto",
      "H. de Guise"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/1464-4266/7/9/008",
    "journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 7 (2005) 283-287",
    "title": "A complementarity-based approach to phase in finite-dimensional quantum   systems",
    "url": "https://arxiv.org/abs/quant-ph/0410135"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eff2ec83-6c2b-4e77-8ecd-a6099cf4284f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}