{
  "id": "cond-mat/0012502",
  "version": "v1",
  "published": "2000-12-28T21:41:06.000Z",
  "updated": "2000-12-28T21:41:06.000Z",
  "title": "A nonextensive critical phenomenon scenario for quantum entanglement",
  "authors": [
    "Constantino Tsallis",
    "Pedro W. Lamberti",
    "Domingo Prato"
  ],
  "comment": "To appear in Physica A, Proceedings of the IUPAP Workshop on New Trends on Fractal Aspects of Complex Systems (16 - 20 October 2000, Maceio-AL, Brazil), ed. M.L. Lyra (Elsevier, Amsterdam, 2001); 8 PS figures",
  "doi": "10.1016/S0378-4371(01)00070-X",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We discuss the paradigmatic bipartite spin-1/2 system having the probabilities $\\frac{1+3x}{4}$ of being in the Einstein-Podolsky-Rosen fully entangled state $|\\Psi^-$$> \\equiv \\frac{1}{\\sqrt 2}(|$$\\uparrow>_A|$$\\downarrow>_B$$-|$$\\downarrow>_A|$$\\uparrow>_B)$ and $\\frac{3(1-x)}{4}$ of being orthogonal. This system is known to be separable if and only if $x\\le1/3$ (Peres criterion). This critical value has been recently recovered by Abe and Rajagopal through the use of the nonextensive entropic form $S_q \\equiv \\frac{1- Tr \\rho^q}{q-1} (q \\in \\cal{R}; $$S_1$$= -$ $Tr$ $ \\rho \\ln \\rho)$ which has enabled a current generalization of Boltzmann-Gibbs statistical mechanics. This result has been enrichened by Lloyd, Baranger and one of the present authors by proposing a critical-phenomenon-like scenario for quantum entanglement. Here we further illustrate and discuss this scenario through the calculation of some relevant quantities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-12-28T21:41:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonextensive critical phenomenon scenario",
      "quantum entanglement",
      "paradigmatic bipartite",
      "einstein-podolsky-rosen fully entangled state",
      "current generalization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}