{
  "id": "1505.04682",
  "version": "v1",
  "published": "2015-05-18T15:26:02.000Z",
  "updated": "2015-05-18T15:26:02.000Z",
  "title": "Monotone Riemannian Metrics and Negativity of Entanglement",
  "authors": [
    "Prasenjit Deb"
  ],
  "comment": "Comments and suggestions welcome",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Monotone Riemannian metrics are very useful for information-theoretic and statistical considerations on the quantum state space. In this article, considering the quantum state space being spanned by 2x2 density matrices, we determine a particular Riemannian metric for a state $\\rho$ . Then we show that if $\\rho$ gets entangled with another quantum state, the negativity of the generated entangled state is, upto a constant factor, equals to square root of that particular Riemannian metric. Our result clearly relates a geometric quantity to a measure of entanglement. Moreover, the result establishes the possibility of understanding quantum correlations through geometric approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-18T15:26:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monotone riemannian metrics",
      "quantum state space",
      "negativity",
      "entanglement",
      "2x2 density matrices"
    ],
    "publication": {
      "doi": "10.1007/s11128-015-1227-2",
      "journal": "Quantum Information Processing",
      "year": 2016,
      "month": "Apr",
      "volume": 15,
      "number": 4,
      "pages": 1629
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016QuIP...15.1629D"
    }
  }
}