{
  "id": "0801.1545",
  "version": "v1",
  "published": "2008-01-10T05:05:58.000Z",
  "updated": "2008-01-10T05:05:58.000Z",
  "title": "Characteristics and benchmarks of entanglement of mixed states -- the two qubit case",
  "authors": [
    "Shanthanu Bhardwaj",
    "V. Ravishankar"
  ],
  "comment": "12 pages, 6 figures. Enlarged version of quant-phy/0703017",
  "doi": "10.1103/PhysRevA.77.022322",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\\mathcal{P}_{\\rho}(\\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as \\textit{concurrence} and \\textit{negativity}) for two qubit systems are rough benchmarks, and not monotones of each other. Focussing on the two qubit states, we provide an explicit construction of $\\mathcal{P}_{\\rho}(\\mathcal{E})$ and show that it is characterised by a set of parameters, of which concurrence is but one particular combination. $\\mathcal{P}_{\\rho}(\\mathcal{E})$ is manifestly invariant under $SU(2) \\times SU(2)$ transformations. It can, in fact, reconstruct the state up to local operations - with the specification of at most four additional parameters. Finally the new measure resolves the controversy regarding the role of entanglement in quantum computation in NMR systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-01-10T05:05:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Mn",
      "03.65.Ud",
      "03.67.Hk",
      "76.60.-k"
    ],
    "keywords": [
      "mixed states",
      "qubit case",
      "entanglement",
      "characteristics",
      "probability density function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2008,
      "month": "Feb",
      "volume": 77,
      "number": 2,
      "pages": "022322"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvA..77b2322B"
    }
  }
}