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Journal of Cryptology

Some improved bounds on the information rate of perfect secret sharing schemes

Ernest F. Brickell, Douglas R. Stinson

Published Oct 1, 1992• 149 citations
Publisher
DOI
10.1007/bf02451112

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The information rate is an important metric of the performance of a quantum-secret-sharing scheme.In this paper,we characterize the quantum access structures by means of the theory of hypergraph.Furthermore,we derive the optimal information rate and the construction of perfect quantum-secret-sharing schemes corresponding to the quantum access structures with at most four players which are given in terms of the relationship between certain access structures and hypergraphs.The exact values for the optimal information rate in 5 of the 13 access structures are computed and the relevant construction of perfect secret sharing schemes is discussed.At the same time,the upper bounds for the information rate of other 8 quantum access structures are computed.