{
  "id": "1903.10745",
  "version": "v1",
  "published": "2019-03-26T09:14:31.000Z",
  "updated": "2019-03-26T09:14:31.000Z",
  "title": "Entangled edge states of corank one with positive partial transposes",
  "authors": [
    "Jinwon Choi",
    "Young-Hoon Kiem",
    "Seung-Hyeok Kye"
  ],
  "comment": "17 pages",
  "categories": [
    "quant-ph",
    "math.OA"
  ],
  "abstract": "We construct a parameterized family of $n\\otimes n$ PPT states of corank one for each $n\\ge 3$. With a suitable choice of parameters, we show that they are $n\\otimes n$ PPT entangled edge states of corank one for $3\\le n\\le 800$. They violate the range criterion for separability in the most extreme way. Note that corank one is the smallest possible corank for such states. The corank of the partial transpose is given by $2n-3$, which is also the smallest possible corank for the partial transposes of PPT entangled edge states of corank one. They provide the first explicit examples of such states for $n\\ge 4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-26T09:14:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P15",
      "15A30",
      "46L05"
    ],
    "keywords": [
      "positive partial transposes",
      "ppt entangled edge states",
      "first explicit examples",
      "ppt states",
      "range criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}