{
  "annotation_id": "44daf1e8-7587-4432-831e-39670b751c60",
  "date_created": "2026-03-02T18:02:09.593000Z",
  "date_modified": "2026-03-02T18:02:09.593000Z",
  "file_hash": "cde84996e686ec1af82d02c81f11456d1a75cc025a338de79e3c3f7efde2641a",
  "private": false,
  "record": {
    "abstract": "Bell-type inequalities and violations thereof reveal the fundamental\ndifferences between standard probability theory and its quantum counterpart. In\nthe course of previous investigations ultimate bounds on quantum mechanical\nviolations have been found. For example, Tsirelson\u0027s bound constitutes a global\nupper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and\nthe Clauser-Horne (CH) inequalities. Here we investigate a method for\ncalculating the precise quantum bounds on arbitrary Bell-type inequalities by\nsolving the eigenvalue problem for the operator associated with each Bell-type\ninequality. Thereby, we use the min-max principle to calculate the norm of\nthese self-adjoint operators from the maximal eigenvalue yielding the upper\nbound for a particular set of measurement parameters. The eigenvectors\ncorresponding to the maximal eigenvalues provide the quantum state for which a\nBell-type inequality is maximally violated.",
    "arxiv_id": "quant-ph/0407145",
    "authors": [
      "Stefan Filipp",
      "Karl Svozil"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1874561",
    "journal_ref": "AIP Conference Proceedings 750. Foundations of Probability and\n  Physics-3, ed. by Andrei Khrennikov (American Institute of Physics,Melville,\n  NY, 2005), pp. 87-94.",
    "title": "Tracing the bounds on Bell-type inequalities",
    "url": "https://arxiv.org/abs/quant-ph/0407145"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "78095aed-ec69-4c36-954d-69facfb9e362",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}