{
  "annotation_id": "ab8862fe-f7f0-42a3-8257-9423fa37c433",
  "date_created": "2026-03-02T18:01:39.141000Z",
  "date_modified": "2026-03-02T18:01:39.141000Z",
  "file_hash": "e7a3277f61c7e59628617d42ffabe9189d0c7cc7ed63aa11ff9468c1de1641e1",
  "private": false,
  "record": {
    "abstract": "A bipartite spin-1/2 system having the probabilities $\\frac{1+3x}{4}$ of\nbeing in the Einstein-Podolsky-Rosen entangled state $|\\Psi^-$$\u003e \\equiv\n\\frac{1}{\\sqrt\n2}(|$$\\uparrow\u003e_A|$$\\downarrow\u003e_B$$-|$$\\downarrow\u003e_A|$$\\uparrow\u003e_B)$ and\n$\\frac{3(1-x)}{4}$ of being orthogonal, is known to admit a local realistic\ndescription if and only if $x\u003c1/3$ (Peres criterion). We consider here a more\ngeneral case where the probabilities of being in the entangled states\n$|\\Phi^{\\pm}$$\u003e \\equiv \\frac{1}{\\sqrt 2}(|$$\\uparrow\u003e_A|$$\\uparrow\u003e_B \\pm\n|$$\\downarrow\u003e_A|$$\\downarrow\u003e_B)$ and $|\\Psi^{\\pm}$$\u003e \\equiv \\frac{1}{\\sqrt\n2}(|$$\\uparrow\u003e_A|$$\\downarrow\u003e_B \\pm |$$\\downarrow\u003e_A|$$\\uparrow\u003e_B)$ (Bell\nbasis) are given respectively by $\\frac{1-x}{4}$, $\\frac{1-y}{4}$,\n$\\frac{1-z}{4}$ and $\\frac{1+x+y+z}{4}$. Following Abe and Rajagopal, we use\nthe nonextensive entropic form $S_q \\equiv \\frac{1- Tr \\rho^q}{q-1} (q \\in\n\\cal{R}; $$S_1$$= -$ $Tr$ $ \\rho \\ln \\rho)$ which has enabled a current\ngeneralization of Boltzmann-Gibbs statistical mechanics, and determine the\nentire region in the $(x,y,z)$ space where local realism is admissible. For\ninstance, in the vicinity of the EPR state, classical realism is possible if\nand only if $x+y+z\u003c1$, which recovers Peres\u0027 criterion when $x=y=z$. In the\nvicinity of the other three states of the Bell basis, the situation is\nidentical. A critical-phenomenon-like scenario emerges. These results\nillustrate the computational power of this new nonextensive-quantum-information\nprocedure.",
    "arxiv_id": "quant-ph/0007112",
    "authors": [
      "Constantino Tsallis",
      "Seth Lloyd",
      "Michel Baranger"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Generalization of the Peres criterion for local realism through   nonextensive entropy",
    "url": "https://arxiv.org/abs/quant-ph/0007112"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5f05b43b-050b-4d71-be3d-80d1d9c878f4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}