{
  "annotation_id": "07b8a333-bf4b-40e7-a0fb-13a93fa4fd57",
  "date_created": "2026-03-02T18:01:52.228000Z",
  "date_modified": "2026-03-02T18:01:52.228000Z",
  "file_hash": "b58a5ce5cf6880421c5f88d78abd1c72f09aa18285b09bc8a53b5bf55e2d02d5",
  "private": false,
  "record": {
    "abstract": "We derive ``Bell inequalities\u0027\u0027 in four dimensional phase space and prove the\nfollowing ``three marginal theorem\u0027\u0027 for phase space densities\n$\\rho(\\overrightarrow{q},\\overrightarrow{p})$, thus settling a long standing\nconjecture : ``there exist quantum states for which more than three of the\nquantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and\n$(p_1,q_2)$ cannot be reproduced as marginals of a positive\n$\\rho(\\overrightarrow{q},\\overrightarrow{p})$\u0027\u0027. We also construct the most\ngeneral positive $\\rho(\\overrightarrow{q},\\overrightarrow{p})$ which reproduces\nany three of the above quantum probability densities for arbitrary quantum\nstates. This is crucial for the construction of a maximally realistic quantum\ntheory.",
    "arxiv_id": "quant-ph/0205157",
    "authors": [
      "G. Auberson",
      "G. Mahoux",
      "S. M. Roy",
      "Virendra Singh"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0375-9601(02)00827-7",
    "title": "Bell Inequalities in Phase Space and their Violation in Quantum   Mechanics",
    "url": "https://arxiv.org/abs/quant-ph/0205157"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a55ad4a0-bc31-46bd-95fc-b141b7b19258",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}