{
  "id": "quant-ph/0605079",
  "version": "v1",
  "published": "2006-05-08T17:25:55.000Z",
  "updated": "2006-05-08T17:25:55.000Z",
  "title": "Geometrical aspects of entanglement",
  "authors": [
    "Jon Magne Leinaas",
    "Jan Myrheim",
    "Eirik Ovrum"
  ],
  "comment": "31 pages, 6 figures",
  "doi": "10.1103/PhysRevA.74.012313",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and non-unitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability, and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-05-08T17:25:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density matrices",
      "composite system",
      "similar approach works",
      "study geometrical aspects",
      "bound entanglement"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}