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Access Structure in Graphs in High Dimension and Application to Secret Sharing Marin, Anne Markham, Damian Perdrix, Simon Quantum Secret Sharing Graph State Multigraph Access structure 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Anne Marin and Damian Markham and Simon Perdrix 2013 Is Part Of LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TQC.2013.308 urn:nbn:de:0030-drops-43306 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.308 eng https://creativecommons.org/licenses/by/3.0/legalcode