{
  "id": "quant-ph/0503052",
  "version": "v2",
  "published": "2005-03-04T18:40:56.000Z",
  "updated": "2005-10-18T14:06:47.000Z",
  "title": "Minimum orbit dimension for local unitary action on n-qubit pure states",
  "authors": [
    "David W. Lyons",
    "Scott N. Walck"
  ],
  "comment": "19 pages",
  "journal": "J. Math. Phys. 46(10):102106, 2005",
  "doi": "10.1063/1.2048327",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-10-18T14:06:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local unitary action",
      "minimum orbit dimension",
      "n-qubit pure states",
      "local unitary transformations partitions",
      "n-qubit quantum state space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}