{
  "id": "1303.5570",
  "version": "v3",
  "published": "2013-03-22T10:13:26.000Z",
  "updated": "2014-08-13T16:08:23.000Z",
  "title": "Computable measure of the quantum correlation",
  "authors": [
    "S. Javad Akhtarshenas",
    "Hamidreza Mohammadi",
    "Saman Karimi",
    "Zahra Azmi"
  ],
  "comment": "14 pages, Title and Abstract are changed, Sections I, III are modified, Two figures are added, Appendices A and B are added, Conclusion is refined",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A general state of an $m\\otimes n$ system is a classical-quantum state if and only if its associated $A$-correlation matrix (a matrix constructed from the coherence vector of the party $A$, the correlation matrix of the state, and a function of the local coherence vector of the subsystem $B$), has rank no larger than $m-1$. Using the general Schatten $p$-norms, we quantify quantum correlation by measuring any violation of this condition. The required minimization can be carried out for the general $p$-norms and any function of the local coherence vector of the unmeasured subsystem, leading to a class of computable quantities which can be used to capture the quantumness of correlations due to the subsystem $A$. We introduce two special members of these quantifiers; The first one coincides with the tight lower bound on the geometric measure of discord, so that such lower bound fully captures the quantum correlation of a bipartite system. Accordingly, a vanishing tight lower bound on the geometric discord is a necessary and sufficient condition for a state to be zero-discord. The second quantifier has the property that it is invariant under a local and reversible operation performed on the unmeasured subsystem, so that it can be regarded as a computable well-defined measure of the quantum correlations. The approach presented in this paper provides a way to circumvent the problem with the geometric discord. We provide some examples to exemplify this measure.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-08-13T16:08:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum correlation",
      "computable measure",
      "tight lower bound",
      "local coherence vector",
      "correlation matrix"
    ],
    "publication": {
      "doi": "10.1007/s11128-014-0839-2",
      "journal": "Quantum Information Processing",
      "year": 2015,
      "month": "Jan",
      "volume": 14,
      "number": 1,
      "pages": 247
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015QuIP...14..247A"
    }
  }
}