{
  "id": "1109.1487",
  "version": "v1",
  "published": "2011-09-07T15:17:17.000Z",
  "updated": "2011-09-07T15:17:17.000Z",
  "title": "New Protocols and Lower Bound for Quantum Secret Sharing with Graph States",
  "authors": [
    "Jérôme Javelle",
    "Mehdi Mhalla",
    "Simon Perdrix"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "We introduce a new family of quantum secret sharing protocols with limited quantum resources which extends the protocols proposed by Markham and Sanders and by Broadbent, Chouha, and Tapp. Parametrized by a graph G and a subset of its vertices A, the protocol consists in: (i) encoding the quantum secret into the corresponding graph state by acting on the qubits in A; (ii) use a classical encoding to ensure the existence of a threshold. These new protocols realize ((k,n)) quantum secret sharing i.e., any set of at least k players among n can reconstruct the quantum secret, whereas any set of less than k players has no information about the secret. In the particular case where the secret is encoded on all the qubits, we explore the values of k for which there exists a graph such that the corresponding protocol realizes a ((k,n)) secret sharing. We show that for any threshold k> n-n^{0.68} there exists a graph allowing a ((k,n)) protocol. On the other hand, we prove that for any k< 79n/156 there is no graph G allowing a ((k,n)) protocol. As a consequence there exists n_0 such that the protocols introduced by Markham and Sanders admit no threshold k when the secret is encoded on all the qubits and n>n_0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-07T15:17:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lower bound",
      "quantum secret sharing protocols",
      "limited quantum resources",
      "protocol consists",
      "corresponding graph state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1487J"
    }
  }
}