License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.TQC.2013.308
URN: urn:nbn:de:0030-drops-43306
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4330/
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Marin, Anne ; Markham, Damian ; Perdrix, Simon

Access Structure in Graphs in High Dimension and Application to Secret Sharing

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Abstract

We give graphical characterisation of the access structure to both classical and quantum information encoded onto a multigraph defined for prime dimension q, as well as explicit decoding operations for quantum secret sharing based on graph state protocols. We give a lower bound on $k$ for the existence of a ((k,n))_q scheme and prove, using probabilistic methods, that there exists alpha such that a random multigraph has an accessing parameter k => alpha*n with high probability.

BibTeX - Entry

@InProceedings{marin_et_al:LIPIcs:2013:4330,
  author =	{Anne Marin and Damian Markham and Simon Perdrix},
  title =	{{Access Structure in Graphs in High Dimension and Application to Secret Sharing}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{308--324},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Simone Severini and Fernando Brandao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4330},
  URN =		{urn:nbn:de:0030-drops-43306},
  doi =		{10.4230/LIPIcs.TQC.2013.308},
  annote =	{Keywords: Quantum Secret Sharing, Graph State, Multigraph, Access structure}
}

Keywords: Quantum Secret Sharing, Graph State, Multigraph, Access structure
Collection: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Issue Date: 2013
Date of publication: 13.11.2013

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