{
  "id": "0809.4276",
  "version": "v5",
  "published": "2008-09-25T10:11:27.000Z",
  "updated": "2008-12-07T16:20:30.000Z",
  "title": "Entanglement properties of topological color codes",
  "authors": [
    "Mehdi Kargarian"
  ],
  "comment": "12 pages, 6 figures",
  "journal": "Phys. Rev. A 78, 062312 (2008)",
  "doi": "10.1103/PhysRevA.78.062312",
  "categories": [
    "quant-ph",
    "cond-mat.str-el",
    "hep-th"
  ],
  "abstract": "The entanglement properties of a class of topological stabilizer states, the so called \\emph{topological color codes} defined on a two-dimensional lattice or \\emph{2-colex}, are calculated. The topological entropy is used to measure the entanglement of different bipartitions of the 2-colex. The dependency of the ground state degeneracy on the genus of the surface shows that the color code can support a topological order, and the contribution of the color in its structure makes it interesting to compare with the Kitaev's toric code. While a qubit is maximally entangled with rest of the system, two qubits are no longer entangled showing that the color code is genuinely multipartite entangled. For a convex region, it is found that entanglement entropy depends only on the degrees of freedom living on the boundary of two subsystems. The boundary scaling of entropy is supplemented with a topological subleading term which for a color code defined on a compact surface is twice than the toric code. From the entanglement entropy we construct a set of bipartitions in which the diverging term arising from the boundary term is washed out, and the remaining non-vanishing term will have a topological nature. Besides the color code on the compact surface, we also analyze the entanglement properties of a version of color code with border, i.e \\emph{triangular color code}.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2008-12-07T16:20:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Lx",
      "03.67.-a",
      "03.67.Mn",
      "03.65.Ud",
      "42.50.Dv"
    ],
    "keywords": [
      "entanglement properties",
      "topological color codes",
      "compact surface",
      "kitaevs toric code",
      "entanglement entropy depends"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2008,
      "month": "Dec",
      "volume": 78,
      "number": 6,
      "pages": "062312"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 797672,
      "adsabs": "2008PhRvA..78f2312K"
    }
  }
}