{
  "id": "quant-ph/0703063",
  "version": "v1",
  "published": "2007-03-07T17:37:46.000Z",
  "updated": "2007-03-07T17:37:46.000Z",
  "title": "Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach",
  "authors": [
    "Maurice de Gosson",
    "Franz Luef"
  ],
  "comment": "To appear in Lett. Math. Phys",
  "doi": "10.1007/s11005-007-0150-6",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy's formulation of the uncertainty principle for a function and its Fourier transform. As a consequence we are able to state a more general form of Hardy's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-07T17:37:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertainty principle",
      "hardys formulation",
      "symplectic approach",
      "phase space gaussian",
      "wigner distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}