{
  "annotation_id": "237f0077-d907-4060-8075-7606d7ae69d1",
  "date_created": "2026-03-02T18:02:10.346000Z",
  "date_modified": "2026-03-02T18:02:10.346000Z",
  "file_hash": "5cdc6b0f3b7040441d0868848d6192d471cefc2e03ff717b0f37b5d7ee4bfe9a",
  "private": false,
  "record": {
    "abstract": "In their 1936 founding paper on quantum logic, Birkhoff and von Neumann\npostulated that the lattice describing the experimental propositions concerning\na quantum system is orthocomplemented. We prove that this postulate fails for\nthe lattice L_sep describing a compound system consisting of so called\nseparated quantum systems. By separated we mean two systems prepared in\ndifferent ``rooms\u0027\u0027 of the lab, and before any interaction takes place. In that\ncase the state of the compound system is necessarily a product state. As a\nconsequence, Dirac\u0027s superposition principle fails, and therefore L_sep cannot\nsatisfy all Piron\u0027s axioms. In previous works, assuming that L_sep is\northocomplemented, it was argued that L_sep is not orthomodular and fails to\nhave the covering property. Here we prove that L_sep cannot admit and\northocomplementation. Moreover, we propose a natural model for L_sep which has\nthe covering property.",
    "arxiv_id": "quant-ph/0410085",
    "authors": [
      "Boris Ischi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s10773-005-8016-0",
    "title": "Orthocomplementation and compound systems",
    "url": "https://arxiv.org/abs/quant-ph/0410085"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4bd15343-06c7-437b-962b-d0bf030f7f04",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}