{
  "id": "1110.1054",
  "version": "v2",
  "published": "2011-10-05T17:43:31.000Z",
  "updated": "2012-01-25T20:14:17.000Z",
  "title": "Why the Entanglement of Formation is not generally monogamic",
  "authors": [
    "F. F. Fanchini",
    "M. C. de Oliveira",
    "L. K. Castelano",
    "M. F. Cornelio"
  ],
  "comment": "7 pages, 3 figures. Extended version",
  "journal": "Phys. Rev. A 87, 032317 (2013)",
  "doi": "10.1103/PhysRevA.87.032317",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Differently from correlation of classical systems, entanglement of quantum systems cannot be distributed at will - if one system A is maximally entangled with another system B, it cannot be entangled at all to a third system C. This concept, known as the monogamy of entanglement, manifests when the entanglement of A with a pair BC, can be divided as contributions of entanglement between A and B and A and C, plus a term \\tau_{ABC} involving genuine tripartite entanglement and so expected to be always positive. A very important measure in Quantum Information Theory, the Entanglement of Formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for EOF to become a monogamous measure, ie, for \\tau_{ABC} \\ge 0. The relation derived is connected to the discrepancy between quantum and classical correlations, being \\tau_{ABC} negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of EOF to the Squashed Entanglement, an always monogamous entanglement measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-25T20:14:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Mn",
      "03.65.Ud"
    ],
    "keywords": [
      "arbitrary pure tripartite state",
      "quantum correlation prevails",
      "genuine tripartite entanglement",
      "quantum information theory",
      "pair bc"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2013,
      "month": "Mar",
      "volume": 87,
      "number": 3,
      "pages": "032317"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013PhRvA..87c2317F"
    }
  }
}