{
  "id": "1307.1362",
  "version": "v1",
  "published": "2013-07-04T14:54:39.000Z",
  "updated": "2013-07-04T14:54:39.000Z",
  "title": "Geometry for separable states and construction of entangled states with positive partial transposes",
  "authors": [
    "Kil-Chan Ha",
    "Seung-Hyeok Kye"
  ],
  "comment": "8 pages, 2 figures",
  "journal": "Physical Review A, 88, 024302 (2013)",
  "doi": "10.1103/PhysRevA.88.024302",
  "categories": [
    "quant-ph",
    "math.OA"
  ],
  "abstract": "We construct faces of the convex set of all $2\\otimes 4$ bipartite separable states, which are affinely isomorphic to the simplex $\\Delta_{9}$ with ten extreme points. Every interior point of these faces is a separable state which has a unique decomposition into 10 product states, even though ranks of the state and its partial transpose are 5 and 7, respectively. We also note that the number 10 is greater than $2\\times 4$, to disprove a conjecture on the lengths of qubit-qudit separable states. This face is inscribed in the corresponding face of the convex set of all PPT states so that sub-simplices $\\Delta_k$ of $\\Delta_{9}$ share the boundary if and only if $k\\le 5$. This enables us to find a large class of $2\\otimes 4$ PPT entangled edge states with rank five.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-04T14:54:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P15",
      "15A30",
      "46L05",
      "03.67.Mn",
      "03.65.Ud",
      "02.40.Ft"
    ],
    "keywords": [
      "positive partial transposes",
      "entangled states",
      "construction",
      "convex set",
      "ppt entangled edge states"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2013,
      "month": "Aug",
      "volume": 88,
      "number": 2,
      "pages": "024302"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvA..88b4302H"
    }
  }
}