{
  "annotation_id": "9b90fcd2-6e11-4909-ade4-d666f438e3db",
  "date_created": "2026-03-02T18:01:42.363000Z",
  "date_modified": "2026-03-02T18:01:42.363000Z",
  "file_hash": "d4cf02572ad1c241bd84bacb14180a6f3624380cc2cd1c9b1b4fa066322a196d",
  "private": false,
  "record": {
    "abstract": "We show how to construct states for which a Greenberger-Horne-Zeilinger type\nparadox occurs if each party measures either the position or momentum of his\nparticle. The paradox can be ascribed to the anticommutation of certain\ntranslation operators in phase space. We then rephrase the paradox in terms of\nmodular and binary variables. The origin of the paradox is then due to the fact\nthat the associativity of addition of modular variables is true only for\nc-numbers but does not hold for operators.",
    "arxiv_id": "quant-ph/0103048",
    "authors": [
      "Serge Massar",
      "Stefano Pironio"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.062108",
    "journal_ref": "Phys. Rev. A 64, 062108 (2001)",
    "title": "Greenberger-Horne-Zeilinger paradox for continuous variables",
    "url": "https://arxiv.org/abs/quant-ph/0103048"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8a36b965-c577-454e-be20-3436939bdf73",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}