{
  "annotation_id": "22082dff-d053-4e3f-b7e4-94b69f2e74bb",
  "date_created": "2026-03-02T18:01:42.411000Z",
  "date_modified": "2026-03-02T18:01:42.411000Z",
  "file_hash": "f75a09e333d0a70ce3fc7823e9660a701c26030a64d7743a1d9c56b4b7dd510e",
  "private": false,
  "record": {
    "abstract": "We demonstrate the quantum probabilistic rule (which differ from classical\nBayes\u0027 formula by the cosinus factor) can be obtained on purely classical basis\nas a consequence of the perturbation effect of preparation procedures. In any\ncase the interference can be easily simulated for macrosystems. Moreover, we\nobtain the classification of all possible transformations of probablities which\ncan arise via perturbation effects. There are two main transformation classes:\nwith trigonometric and hyperbolic (\"interference\") perturbations of classical\nBayes\u0027 formula. Quantum probabilistic rule is just a particular case of\ntrigonometric probablistic behaviour. Hyperbolic probablistic behaviour can be\neasily simulated. However, the question of its observation for \"real physical\nphenomena\" is open.",
    "arxiv_id": "quant-ph/0011104",
    "authors": [
      "Andrei Khrennikov"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "On the mystery of quantum probabilistic rule: trigonometric and   hyperbolic probabilistic behaviours",
    "url": "https://arxiv.org/abs/quant-ph/0011104"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a5c70e1c-e0d7-4535-8f5e-def7c1f7940d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}