含至多四个参与者的量子秘密共享方案的最优信息率

信息率是衡量量子秘密共享方案性能的一个重要指标.在本文中,我们利用超图的相关理论刻画了量子存取结构.然后,利用超图和量子存取结构间的关系给出了参与者人数至多为4的所有13个量子存取结构,并基于量子信息论研究了其最优信息率及所对应的完善的量子秘密共享方案.对其中的5种存取结构的最优信息率的准确值进行了计算,并讨论了达到此信息率的方案的具体构造;对余下的8种存取结构的最优信息率的上界进行了计算.

The Optimal Information Rate of Quantum-Secret-Sharing Schemes Based on at Most Four Participants

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.