{
  "id": "1810.03125",
  "version": "v1",
  "published": "2018-10-07T11:47:21.000Z",
  "updated": "2018-10-07T11:47:21.000Z",
  "title": "On the decomposition of the supersymmetric state",
  "authors": [
    "Qian Lilong",
    "Chu Delin"
  ],
  "categories": [
    "quant-ph",
    "math.OC"
  ],
  "abstract": "In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this decomposition is a supersymmetric pure product state $|x,x\\rangle\\langle x,x|$, which are called S-separable. We conjecture that any supersymmetric states are S-separable and we prove that this conjecture holds when the rank is less than or equal to 3 or $N$. Moreover, we propose another weaker conjecture that any separable supersymmetric states are S-separable. It was proved to be true when the rank is less than or equal to $4$ or $N+1$. We also propose a numerical algorithm which is able to detect S-separability. Besides, we analysis the convergence behavior of this algorithm. Some numerical examples are tested to show the effectiveness of the algorithm.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-07T11:47:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decomposition",
      "supersymmetric pure product state",
      "multipartite system",
      "weaker conjecture",
      "conjecture holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}