{
  "id": "1107.1023",
  "version": "v3",
  "published": "2011-07-06T04:32:09.000Z",
  "updated": "2011-11-22T11:24:43.000Z",
  "title": "Existence of product vectors and their partial conjugates in a pair of spaces",
  "authors": [
    "Young-Hoon Kiem",
    "Seung-Hyeok Kye",
    "Jungseob Lee"
  ],
  "comment": "15 pages, to correct a technical problem in V2",
  "journal": "J. Math. Phys. 52, 122201 (2011)",
  "categories": [
    "quant-ph",
    "math.OA"
  ],
  "abstract": "Let $D$ and $E$ be subspaces of the tensor product of the $m$ and $n$ dimensional complex spaces, with codimensions $k$ and \\ell$, respectively. We show that if $k+\\ell<m+n-2$ then there must exist a product vector in $D$ whose partial conjugate lies in $E$. If $k+\\ell >m+n-2$ then there may not exist such a product vector. If $k+\\ell=m+n-2$ then both cases may occur depending on $k$ and $\\ell$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-11-22T11:24:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P15",
      "15A30",
      "46L05",
      "03.65.Ta",
      "03.65.Ud"
    ],
    "keywords": [
      "partial conjugates",
      "product vectors",
      "dimensional complex spaces",
      "tensor product"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "doi": "10.1063/1.3663835",
      "year": 2011,
      "month": "Dec",
      "volume": 52,
      "number": 12,
      "pages": 2201
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JMP....52l2201K"
    }
  }
}