{
  "annotation_id": "57593b3a-8e17-4758-b70a-b1ffc7d4dc6b",
  "date_created": "2026-03-02T18:01:41.706000Z",
  "date_modified": "2026-03-02T18:01:41.706000Z",
  "file_hash": "4d99929f46423584971237927dfa50a78195dd29abc964097b22d8b9b821cd70",
  "private": false,
  "record": {
    "abstract": "We show that one can formulate an algebra with lattice ordering so as to\ncontain one quantum and five classical operations as opposed to the standard\nformulation of the Hilbert space subspace algebra. The standard orthomodular\nlattice is embeddable into the algebra. To obtain this result we devised\nalgorithms and computer programs for obtaining expressions of all quantum and\nclassical operations within an orthomodular lattice in terms of each other,\nmany of which are presented in the paper. For quantum disjunction and\nconjunction we prove their associativity in an orthomodular lattice for any\ntriple in which one of the elements commutes with the other two and their\ndistributivity for any triple in which a particular one of the elements\ncommutes with the other two. We also prove that the distributivity of symmetric\nidentity holds in Hilbert space, although it remains an open problem whether it\nholds in all orthomodular lattices, as it does not fail in any of over 50\nmillion Greechie diagrams we tested.",
    "arxiv_id": "quant-ph/0103135",
    "authors": [
      "Norman D. Megill",
      "Mladen Pavicic"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "journal_ref": "International Journal of Theoretical Physics, 40, 1387-1410 (2001)",
    "title": "Orthomodular Lattices and a Quantum Algebra",
    "url": "https://arxiv.org/abs/quant-ph/0103135"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cdd58a2-ccc2-47ca-af9f-014eeda99ffb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}