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An information theoretic model for quantum secret sharing schemes

J. Mueller-Quade, A. Nascimento, Andreas Winter, Pim Tuyls, H. Imai

Published Jan 1, 2005• 0 citations
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In this paper we introduce a quantum information theoretical model for quantum secret sharing schemes. We show that quantum information theory provides a unifying framework for the study of these schemes. We prove that the information theoretical requirements for a class of quantum secret sharing schemes reduce to only one requirement (the recoverability condition) as a consequence of the no-cloning principle. We give also a shorter proof of the fact that the size of the shares in a quantum secret sharing scheme must be at least as large as the secret itself.
Similarly to earlier models for quantum error correcting codes, we introduce a quantum information theoretical model for quantum secret sharing schemes. This model provides new insights into the theory of quantum secret sharing. By using our model, among other results, we give a shorter proof of Gottesman's theorem that the size of the shares in a quantum secret sharing scheme must be as large as the secret itself. Also, we introduced approximate quantum secret sharing schemes and showed robustness of quantum secret sharing schemes by extending Gottesman's theorem to the approximate case.
Recently, an information theoretical model for quantum secret sharing (QSS) schemes was introduced. By using this model, we prove that pure state quantum threshold schemes (QTS) can be constructed from quantum MDS codes and vice versa. In particular, we consider stabilizer codes and give a constructive proof of their relation with QTS. Furthermore, we reformulate the monotone span program (MSP) construction according to the information theoretical model and check the recoverability and secrecy requirement. Finally, we consider QSS schemes which are based on quantum teleportation