Quantum secret sharing for general access structures

Abstract

We explore the conversion of classical secret-sharing schemes to quantum ones, and how this can be used to give efficient QSS schemes for general adversary structures. Our first result is that quantum secret-sharing is possible for any structure for which no two disjoint sets can reconstruct the secret (this was also proved, somewhat differently, by D. Gottesman). To obtain this we show that a large class of linear classical SS schemes can be converted into quantum schemes of the same efficiency. We also give a necessary and sufficient condiion for the direct conversion of classical schemes into quantum ones, and show that all group homomorphic schemes satisfy it.