LIPIcs.TQC.2013.308.pdf
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Access Structure in Graphs in High Dimension and Application to Secret Sharing
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8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
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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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
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.
Subject Classification
Keywords
- Quantum Secret Sharing
- Graph State
- Multigraph
- Access structure
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