{
  "id": "1406.4954",
  "version": "v1",
  "published": "2014-06-19T06:48:05.000Z",
  "updated": "2014-06-19T06:48:05.000Z",
  "title": "Indecomposability of entanglement witnesses constructed from any permutations",
  "authors": [
    "Xiao-Fei Qi",
    "Jin-Chuan Hou"
  ],
  "comment": "11 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Let $n\\geq 2$ and $\\Phi_{n,t,\\pi}: M_n({\\mathbb C}) \\rightarrow M_n({\\mathbb C})$ be a linear map defined by $\\Phi_{n,t,\\pi}(A)=(n-t)\\sum_{i=1}^nE_{ii}AE_{ii}+t\\sum_{i=1}^nE_{i,\\pi(i)}AE_{i,\\pi(i)}^\\dag-A$, where $0\\leq t\\leq n$, $E_{ij}$s are the matrix units and $\\pi$ is a non-identity permutation of $(1,2,\\cdots,n)$. Denote by $\\{{ F}_s: s=1,2\\ldots, k\\}$ the set of all minimal cycles of $\\pi$ and $l(\\pi)=\\max\\{\\# { F}_s: s=1,2,\\ldots,k\\}$ the length of $\\pi$. It is shown that the Hermitian matrix $W_{n,t,\\pi}$ induced by $\\Phi_{n,t,\\pi}$ is an indecomposable entanglement witness if and only if $\\pi^2\\not={\\rm id}$ (the identity permutation) and $0<t\\leq\\frac{n}{l(\\pi)}$. Some new bounded entangled states are detected by such witnesses that cannot be distinguished by PPT criterion, realignment criterion, etc..",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-19T06:48:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement witnesses",
      "indecomposability",
      "linear map",
      "ppt criterion",
      "matrix units"
    ],
    "publication": {
      "doi": "10.1007/s11128-015-1007-z",
      "journal": "Quantum Information Processing",
      "year": 2015,
      "month": "Jul",
      "volume": 14,
      "number": 7,
      "pages": 2499
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015QuIP...14.2499Q"
    }
  }
}