The quantum secret sharing schemes based on hyperstar access structures

In this paper, we discuss in some detail how the quantum secret sharing schemes based on a class of irregular quantum network structures are designed, where these structures are consisting of hyperstar access structures with three hyper-edges. Firstly, two kinds of classical secret sharing schemes are explicitly established for these irregular network structures. Moreover, these shares from the participants in these classical secret sharing schemes are implemented by the quantum secret sharing scheme, i.e. the parameters of the unitary transformation used in the quantum secret sharing schemes are shares of the corresponding participants in these classical secret sharing schemes. Since these schemes are constructed based on the irregular network structures with the optimal information rate, these constructed quantum secret sharing schemes also have the highest efficiency. Meanwhile, the identity authentication of these protocols ensures their security, making these schemes feasible and more practical using current technology.