{
  "id": "1301.7558",
  "version": "v1",
  "published": "2013-01-31T09:22:35.000Z",
  "updated": "2013-01-31T09:22:35.000Z",
  "title": "Optimality of a class of entanglement witnesses for $3\\otimes 3$ systems",
  "authors": [
    "Xiaofei Qi",
    "Jinchuan Hou"
  ],
  "comment": "12 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Let $\\Phi_{t,\\pi}: M_3({\\mathbb C}) \\rightarrow M_3({\\mathbb C})$ be a linear map defined by $\\Phi_{t,\\pi}(A)=(3-t)\\sum_{i=1}^3E_{ii}AE_{ii}+t\\sum_{i=1}^3E_{i,\\pi(i)}AE_{i,\\pi(i)}^\\dag-A$, where $0\\leq t\\leq 3$ and $\\pi$ is a permutation of $(1,2,3)$. We show that the Hermitian matrix $W_{\\Phi_{t,\\pi}}$ induced by $\\Phi_{t,\\pi}$ is an optimal entanglement witness if and only if $t=1$ and $\\pi$ is cyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-31T09:22:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A69",
      "15A86"
    ],
    "keywords": [
      "entanglement witnesses",
      "optimality",
      "optimal entanglement witness",
      "hermitian matrix"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s10773-013-1649-5",
      "journal": "International Journal of Theoretical Physics",
      "year": 2013,
      "month": "Oct",
      "volume": 52,
      "number": 10,
      "pages": 3474
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013IJTP...52.3474Q"
    }
  }
}