A Generalized Information Theoretical Model for Quantum Secret Sharing

An information theoretical model for quantum secret sharing was introduced by H. Imai et al. (Quantum Inf. Comput. 5(1), 69–80 2005), which was analyzed by quantum information theory. In this paper, we analyze this information theoretical model using the properties of the quantum access structure. By the analysis we propose a generalized model definition for the quantum secret sharing schemes. In our model, there are more quantum access structures which can be realized by our generalized quantum secret sharing schemes than those of the previous one. In addition, we also analyse two kinds of important quantum access structures to illustrate the existence and rationality for the generalized quantum secret sharing schemes and consider the security of the scheme by simple examples.