Quantum Information Processing ( IF 2.5 ) Pub Date : 2021-01-25 , DOI: 10.1007/s11128-021-02988-3 Minjin Choi , Soojoon Lee
Quantum secret sharing allows each player to have classical information for secret sharing in quantum mechanical ways. In this work, we construct a class of quantum states on which players can quantumly perform secret-sharing secure against dishonest players as well as eavesdropper. We here call them the genuine secret-sharing states. In addition, we show that if N players share an N-party genuine secret-sharing state, then arbitrary M players out of the total players can share an M-party genuine secret-sharing state by means of local operations and classical communication on the state, where \(N > M \ge 2\). We also define the distillable rate with respect to the genuine secret-sharing state and explain the connection between the distillable rate and the relative entropy of entanglement.
中文翻译:
真正的秘密共享国家
量子秘密共享允许每个玩家拥有经典信息,以量子力学方式进行秘密共享。在这项工作中,我们构造了一类量子状态,玩家可以在该量子状态上对不诚实的玩家以及窃听者进行秘密共享。我们在这里称它们为真正的秘密共享国家。此外,我们表明,如果N个玩家共享N个缔约方真正的秘密共享状态,则所有玩家中的任意M个玩家都可以通过本地操作和传统通信方式共享M个缔约方真正的秘密共享状态。状态,其中\(N> M \ ge 2 \)。我们还定义了与真实秘密共享状态有关的可蒸馏速率,并解释了可蒸馏速率与相对纠缠熵之间的联系。