{
  "id": "1111.5255",
  "version": "v1",
  "published": "2011-11-22T17:11:59.000Z",
  "updated": "2011-11-22T17:11:59.000Z",
  "title": "Constructing all entanglement witnesses from density matrices",
  "authors": [
    "Bang-Hai Wang",
    "Dong-Yang Long"
  ],
  "comment": "5 pages. Added the computing $c_{\\rho_q}^{\\text{max}}$ in detail",
  "journal": "Phys. Rev. A 84, 014303 (2011)",
  "doi": "10.1103/PhysRevA.84.014303",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We demonstrate a general procedure to construct entanglement witnesses for any entangled state. This procedure is based on the trace inequality and a general form of entanglement witnesses, which is in the form $W=\\rho-c_{\\rho} I$, where $\\rho$ is a density matrix, $c_{\\rho}$ is a non-negative number related to $\\rho$, and $I$ is the identity matrix. The general form of entanglement witnesses is deduced from Choi-Jamio{\\l}kowski isomorphism, that can be reinterpreted as that all quantum states can be obtained by a maximally quantum entangled state pass through certain completely positive maps. Furthermore, we provide the necessary and sufficient condition of the entanglement witness $W=\\rho-c_{\\rho}I$ in operation, as well as in theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-22T17:11:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Mn",
      "03.65.Ca",
      "03.65.Ud"
    ],
    "keywords": [
      "density matrices",
      "general form",
      "maximally quantum entangled state pass",
      "construct entanglement witnesses",
      "identity matrix"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2011,
      "month": "Jul",
      "volume": 84,
      "number": 1,
      "pages": "014303"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvA..84a4303W"
    }
  }
}