{
  "id": "1407.0870",
  "version": "v3",
  "published": "2014-07-03T11:36:34.000Z",
  "updated": "2015-07-12T15:42:38.000Z",
  "title": "Characterization and properties of weakly optimal entanglement witnesses",
  "authors": [
    "Bang-Hai Wang",
    "Hai-Ru Xu",
    "Steve Campbell",
    "Simone Severini"
  ],
  "comment": "13 pages, 2 figures, has been extensively redrafted and restructured",
  "journal": "Quantum Information & Computation, Vol.15 No.13&14 (2005)",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Any weakly optimal entanglement witness can be written as the form of $W^{wopt}=\\sigma-c_{\\sigma}^{max} I$, where $c_{\\sigma}^{max}$ is a non-negative number and $I$ is the identity matrix. We show the relation between the weakly optimal witness $W^{wopt}$ and the eigenvalues of the separable states $\\sigma$. Further we give an application of weakly optimal witnesses for constructing entanglement witnesses in a larger Hilbert space by extending the result of [P. Badzi\\c{a}g {\\it et al}, Phys. Rev. A {\\bf 88}, 010301(R) (2013)], and we examine their geometric properties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-20T22:18:28.000Z",
      "abstract": "We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Weakly optimal entanglement witness are of the form $W^{wopt}=\\sigma-c_{\\sigma}^{max} I$, where $c_{\\sigma}$ is a non-negative number and $I$ is the identity matrix, we show the relation between the weakly optimal witness $W^{wopt}$ and the eigenvalues of separable states $\\sigma$. According to the result of [P. Badzi\\c{a}g {\\it et al}, Phys. Rev. A {\\bf 88}, 010301(R) (2013)], we give the classification of weakly optimal witnesses and the method to construct entanglement witnesses in a larger Hilbert space by any witness or any quantum state. Additionally we examine their geometric properties.",
      "comment": "7 pages, 2 figures, to add the reference of recent review of entanglement witnesses",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-07-12T15:42:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weakly optimal entanglement witnesses",
      "properties",
      "characterization",
      "expectation value vanishes",
      "larger hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0870W"
    }
  }
}