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

Marin, Anne; Markham, Damian; Perdrix, Simon

doi:10.4230/LIPIcs.TQC.2013.308

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

Authors Anne Marin, Damian Markham, Simon Perdrix

Part of: Volume: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2013-11-13

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Document Identifiers

DOI: 10.4230/LIPIcs.TQC.2013.308
URN: urn:nbn:de:0030-drops-43306

Subject Classification

Keywords

Quantum Secret Sharing
Graph State
Multigraph
Access structure

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.TQC.2013.308

Author Details

Anne Marin

Damian Markham

Simon Perdrix

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