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DOI: 10.4230/LIPIcs.TQC.2013.308

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

Authors: Anne Marin, Damian Markham, and Simon Perdrix

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

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.

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Anne Marin, Damian Markham, and Simon Perdrix. Access Structure in Graphs in High Dimension and Application to Secret Sharing. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 308-324, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{marin_et_al:LIPIcs.TQC.2013.308,
  author =	{Marin, Anne and Markham, Damian and Perdrix, Simon},
  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 =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.308},
  URN =		{urn:nbn:de:0030-drops-43306},
  doi =		{10.4230/LIPIcs.TQC.2013.308},
  annote =	{Keywords: Quantum Secret Sharing, Graph State, Multigraph, Access structure}
}

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

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