{
  "id": "quant-ph/0109033",
  "version": "v2",
  "published": "2001-09-06T11:37:42.000Z",
  "updated": "2002-03-18T11:11:33.000Z",
  "title": "Four qubits can be entangled in nine different ways",
  "authors": [
    "F. Verstraete",
    "J. Dehaene",
    "B. De Moor",
    "H. Verschelde"
  ],
  "journal": "Phys. Rev. A, 65: 052112 (2002).",
  "doi": "10.1103/PhysRevA.65.052112",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We consider a single copy of a pure four-partite state of qubits and investigate its behaviour under the action of stochastic local quantum operations assisted by classical communication (SLOCC). This leads to a complete classification of all different classes of pure states of four-qubits. It is shown that there exist nine families of states corresponding to nine different ways of entangling four qubits. The states in the generic family give rise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit entanglement distributed among the four parties. The concept of concurrence and 3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to a seven parameter family of entanglement monotones. Finally, the SLOCC operations maximizing all these entanglement monotones are derived, yielding the optimal single copy distillation protocol.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-03-18T11:11:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal single copy distillation protocol",
      "entanglement monotones",
      "stochastic local quantum operations",
      "pure four-partite state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}