{
  "annotation_id": "e95a2506-467b-4150-a5b3-3655d0288f20",
  "date_created": "2026-03-02T18:02:31.190000Z",
  "date_modified": "2026-03-02T18:02:31.190000Z",
  "file_hash": "8e711d73fe81ecce1de4d6f59a178627a3cd77698b4e672db6ffb327721fd549",
  "private": false,
  "record": {
    "abstract": "Reduction of a state of a quantum system to a subsystem gives partial quantum\ninformation about the true state of the total system. Two subalgebras A1 and A2\nof B(H) are called complementary if the traceless subspaces of A1 and A2 are\northogonal (with respect to the Hilbert-Schmidt inner product). When both\nsubalgebras are maximal Abelian, then the concept reduces to complementary\nobservables or mutually unbiased bases. In the paper several characterizations\nof complementary subalgebras are given in the general case and several examples\nare presented. For a 4-level quantum system, the structure of complementary\nsubalgebras can be described very well, the Cartan decomposition of unitaries\nplays a role. It turns out that a measurement corresponding to the Bell basis\nis complementary to any local measurement of the two-qubit-system.",
    "arxiv_id": "quant-ph/0610189",
    "authors": [
      "Denes Petz"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0034-4877(07)00010-9",
    "journal_ref": "Rep. Math. Phys. 59(2007), 209-224.",
    "title": "Complementarity in quantum systems",
    "url": "https://arxiv.org/abs/quant-ph/0610189"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2e8a1cc6-ab7d-40f0-bbed-61773e8fd7ed",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}