{
  "annotation_id": "6bdc1e5d-455f-4c4f-af0c-799f36b565a9",
  "date_created": "2026-03-02T18:02:45.083000Z",
  "date_modified": "2026-03-02T18:02:45.083000Z",
  "file_hash": "ccf9c5d959ab2f3f249d67cc5921a7e3f936762ca303b3f46e2527ba1d4a9317",
  "private": false,
  "record": {
    "abstract": "Besides their use for efficient computation, quantum computers are a base for\nstudying quantum systems that create valid physical theories using mathematics\nand physics. An essential part of the validation process for quantum mechanics\nis the development of a coherent theory of mathematics and quantum mechanics\ntogether. Such a theory should combine mathematical logical concepts with\nquantum mechanics. That this might be possible is shown here by defining truth,\nvalidity, consistency, and completeness for a quantum mechanical version of a\nsimple classical expression enumeration machine described by Smullyan. It is\nseen that for an interpretation based on a Feynman path sum over expression\npath states, truth, consistency, and completeness have different properties\nthan for the classical system. For instance the truth of a sentence S is\ndefined only on the paths containing S. It is undefined elsewhere. Also S and\nits negation can both be true provided they appear on separate paths. This\nsatisfies the definition of consistency. It is seen that validity and\ncompleteness connect the system dynamics to the truth of the sentences. It is\nproved that validity implies consistency. The requirements of validity and\nmaximal completeness strongly restrict the possible dynamics of the system.\nAspects of the existence of a valid, maximally complete dynamics are discussed.\nAn exponentially efficient quantum computer is described that is also valid and\ncomplete.",
    "arxiv_id": "quant-ph/9811055",
    "authors": [
      "Paul Benioff"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.59.4223",
    "journal_ref": "Phys.Rev. A59 (1999) 4223",
    "title": "A simple Example of Definitions of Truth, Validity, Consistency, and   Completeness in Quantum Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/9811055"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6d050bce-7c68-491e-bca7-634736d8627e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}