{
  "id": "1210.6742",
  "version": "v3",
  "published": "2012-10-25T05:12:19.000Z",
  "updated": "2014-11-10T07:44:34.000Z",
  "title": "Tests for quantum contextuality in terms of $q$-entropies",
  "authors": [
    "Alexey E. Rastegin"
  ],
  "comment": "14 pages, two figures. The version 3 matches the journal version",
  "journal": "Quantum Inf. Comput., Vol. 14, 0996-1013 (2014)",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many similar properties to the standard Shannon entropy. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser-Horne-Shimony-Holt (CHSH) and Klyachko-Can-Binicio\\v{g}lu-Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-15T07:19:14.000Z",
      "abstract": "The information-theoretic approach to Bell's theorem is developed with use of the conditional $q$-entropies. The $q$-entropic measures fulfill many properties similarly to the standard ones. In general, both the locality and noncontextuality notions are usually treated with use of the so-called marginal scenarios. These hypotheses lead to the existence of a joint probability distribution, which marginalizes to all particular ones. Assuming the existence of such a joint probability distribution, we derive the family of inequalities of Bell's type in terms of conditional $q$-entropies for all $q\\geq1$. Quantum violations of the new inequalities are exemplified within the Clauser-Horne-Shimony-Holt (CHSH) and Klyachko-Can-Binicio\\v{g}lu-Shumovsky (KCBS) scenarios. An extension to the case of $n$-cycle scenario is briefly mentioned. The new inequalities with conditional $q$-entropies allow to expand a class of probability distributions, for which the nonlocality or contextuality can be detected within entropic formulation. The $q$-entropic inequalities can also be useful in analyzing cases with detection inefficiencies. Using two models of such a kind, we consider some potential advantages of the $q$-entropic formulation.",
      "comment": "14 pages, two figures. The paper is substantially revised. New results are related to the CHSH scenario and the case of detection inefficiencies. Advantages of the $q$-entropic formulation are emphasized. The bibliography is extended and updated",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-11-10T07:44:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum contextuality",
      "joint probability distribution",
      "entropic formulation",
      "conditional",
      "entropic measures fulfill"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.6742R"
    }
  }
}