{
  "id": "1504.03909",
  "version": "v1",
  "published": "2015-04-15T13:47:00.000Z",
  "updated": "2015-04-15T13:47:00.000Z",
  "title": "Entanglement Rényi $α$-entropy",
  "authors": [
    "Yu-Xin Wang",
    "Liang-Zhu Mu",
    "Vlatko Vedral",
    "Heng Fan"
  ],
  "comment": "5 pages, 2 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Entanglement can be well quantified by R\\'{e}nyi $\\alpha$-entropy which is a generalization of the standard von Neumann entropy. Here we study the measure of entanglement R\\'{e}nyi $\\alpha$-entropy for arbitrary two-qubit states. We show that entanglement of two states may be incomparable, contrary to other well-accepted entanglement measures. These facts impose constraint on the convertibility of entangled states by local operations and classical communication. We find that when $\\alpha $ is larger than a critical value, the entanglement measure by R\\'{e}nyi $\\alpha$-entropy is determined solely by concurrence which is a well accepted measure of entanglement. When $\\alpha $ is small, the entanglement R\\'{e}nyi $\\alpha$-entropy of Werner state is obtained. Interestingly, we show that entanglement R\\'{e}nyi $\\alpha$-entropy of Werner state is always less than any pure entangled state when $\\alpha $ is close to zero, even this Werner state is close to a maximally entangled state and the concurrence is larger. We also conclude that the optimal decomposition of a general mixed state cannot be the same for all $\\alpha $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-15T13:47:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement rényi",
      "werner state",
      "entangled state",
      "standard von neumann entropy",
      "arbitrary two-qubit states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}