对孙莹等提出的利用GreenbergerHorneZeilinger态实现的可控量子秘密共享协议AliceBob信道和AliceCharlie信道窃听检测的虚警概率进行分析, 指出该协议窃听检测虚警概率不为0的原因在于窃听检测测量基选择的随机性.然后, 提出一种改进的利用GreenbergerHorneZeilinger态实现的可控量子秘密共享协议, 以确定性的方式选择窃听检测的测量基.理论分析表明, 改进的利用GreenbergerHorneZeilinger态实现的可控量子秘密共享协议不仅能够以原协议2倍的概率发现任何一个内部不可信方, 从而具有更高的安全性, 而且窃听检测虚警概率达到0.

The false alarm probability of eavesdropping checks on both AliceBob quantum channel and AliceCharlie quantum channel in the controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states proposed by Y. Sun et al. is analyzed. The reason why the total false alarm probability of eavesdropping checks in the controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states is not equal to 0 lies in the randomness of measurement basis selection for eavesdropping checks. Afterward, an improved controllable quantum secret sharing protocol using GreenbergerHorneZeilinger states is proposed, based on using deterministic measurement basis for eavesdropping checks. Theoretical analysis shows that compared with the original one, the improved scheme can discover the eavesdropping from any internal dishonest participant with twice probability, and possesses much higher security. Moreover, the total false alarm probability of eavesdropping checks in the improved scheme is equal to 0.