{
  "annotation_id": "3440009f-5bfc-4844-bda7-d6bc5cecf6a7",
  "date_created": "2026-03-02T18:02:38.132000Z",
  "date_modified": "2026-03-02T18:02:38.132000Z",
  "file_hash": "d3cd09ae4a066039ad053e537bdb35ad6d6a03d60719f0276286dd8d1d7d5d7a",
  "private": false,
  "record": {
    "abstract": "We consider the product of infinitely many copies of a spin-$1\\over 2$\nsystem. We construct projection operators on the corresponding nonseparable\nHilbert space which measure whether the outcome of an infinite sequence of\n$\\sigma^x$ measurements has any specified property. In many cases, product\nstates are eigenstates of the projections, and therefore the result of\nmeasuring the property is determined. Thus we obtain a nonprobabilistic quantum\nanalogue to the law of large numbers, the randomness property, and all other\nfamiliar almost-sure theorems of classical probability.",
    "arxiv_id": "quant-ph/9506016",
    "authors": [
      "Sam Gutmann"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1103/PhysRevA.52.3560",
    "title": "Using Classical Probability To Guarantee Properties of Infinite Quantum   Sequences",
    "url": "https://arxiv.org/abs/quant-ph/9506016"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "39787bb3-7a31-49d3-935c-ae590c658fbf",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}