{
  "annotation_id": "c88c1dfe-dbdc-4dc3-9471-d8f8bd849e45",
  "date_created": "2026-03-02T18:02:34.700000Z",
  "date_modified": "2026-03-02T18:02:34.700000Z",
  "file_hash": "a712a6490f23368a7515ac146ad15af4078920fd5356d5d5d736242c52db7784",
  "private": false,
  "record": {
    "abstract": "We express the condition for a phase space Gaussian to be the Wigner\ndistribution of a mixed quantum state in terms of the symplectic capacity of\nthe associated Wigner ellipsoid. Our results are motivated by Hardy\u0027s\nformulation of the uncertainty principle for a function and its Fourier\ntransform. As a consequence we are able to state a more general form of Hardy\u0027s\ntheorem.",
    "arxiv_id": "quant-ph/0703063",
    "authors": [
      "Maurice de Gosson",
      "Franz Luef"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s11005-007-0150-6",
    "title": "Quantum States and Hardy\u0027s Formulation of the Uncertainty Principle : a   Symplectic Approach",
    "url": "https://arxiv.org/abs/quant-ph/0703063"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3b8cb824-24bf-405e-8b73-2d442e44646c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}