{
  "id": "1011.5859",
  "version": "v2",
  "published": "2010-11-26T19:03:39.000Z",
  "updated": "2010-12-11T22:20:30.000Z",
  "title": "Classical Tensors and Quantum Entanglement II: Mixed States",
  "authors": [
    "P. Aniello",
    "J. Clemente-Gallardo",
    "G. Marmo",
    "G. F. Volkert"
  ],
  "comment": "23 pages, 4 figures",
  "journal": "Int.J.Geom.Meth.Mod.Phys.08:853-883,2011",
  "doi": "10.1142/S0219887811005439",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-11T22:20:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q70"
    ],
    "keywords": [
      "mixed states",
      "quantum entanglement",
      "lie groups",
      "define classical tensor fields",
      "local unitary group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "International Journal of Geometric Methods in Modern Physics",
      "year": 2011,
      "volume": 8,
      "number": 4,
      "pages": 853
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 880413,
      "adsabs": "2011IJGMM..08..853A"
    }
  }
}