{
  "id": "1309.4177",
  "version": "v2",
  "published": "2013-09-17T04:15:57.000Z",
  "updated": "2013-09-24T08:16:58.000Z",
  "title": "The number of product vectors and their partial conjugates in a pair of spaces",
  "authors": [
    "Joohan Na"
  ],
  "comment": "12 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $D$ and $E$ be subspaces of the tensor product of the finite-dimensional Hilbert spaces $\\mathbb{C}^m \\otimes \\mathbb{C}^n$. We show that the number of product vectors in $D$ with their partial conjugates in $E$ is uniformly bounded depending only on $m$ and $n$ whenever it is finite. We also give an upper bound in qubit-qunit case which we expect to be sharp.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-24T08:16:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "product vectors",
      "partial conjugates",
      "finite-dimensional hilbert spaces",
      "tensor product",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4177N"
    }
  }
}