{
  "id": "1003.0727",
  "version": "v2",
  "published": "2010-03-03T04:48:46.000Z",
  "updated": "2010-05-23T21:31:29.000Z",
  "title": "On the comparison of volumes of quantum states",
  "authors": [
    "Deping Ye"
  ],
  "journal": "J. Phys. A: Math. Theor. 43 (2010) 315301 (17pp)",
  "doi": "10.1088/1751-8113/43/31/315301",
  "categories": [
    "quant-ph",
    "cs.IT",
    "math-ph",
    "math.FA",
    "math.IT",
    "math.MP"
  ],
  "abstract": "This paper aims to study the $\\a$-volume of $\\cK$, an arbitrary subset of the set of $N\\times N$ density matrices. The $\\a$-volume is a generalization of the Hilbert-Schmidt volume and the volume induced by partial trace. We obtain two-side estimates for the $\\a$-volume of $\\cK$ in terms of its Hilbert-Schmidt volume. The analogous estimates between the Bures volume and the $\\a$-volume are also established. We employ our results to obtain bounds for the $\\a$-volume of the sets of separable quantum states and of states with positive partial transpose (PPT). Hence, our asymptotic results provide answers for questions listed on page 9 in \\cite{K. Zyczkowski1998} for large $N$ in the sense of $\\a$-volume. \\vskip 3mm PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.Mn",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-23T21:31:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "comparison",
      "hilbert-schmidt volume",
      "3mm pacs numbers",
      "asymptotic results",
      "arbitrary subset"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Aug",
      "volume": 43,
      "number": 31,
      "pages": 315301
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JPhA...43E5301Y"
    }
  }
}