Tang Jie, Ma Song-Ya, Li Qi
School of Mathematics and Statistics, Henan University, Kaifeng 475004, China.
Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Entropy (Basel). 2022 Aug 4;24(8):1077. doi: 10.3390/e24081077.
By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents' assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.
通过利用非最大纠缠四量子比特簇态作为量子信道，我们首先提出了一种将任意三量子比特态以一定概率在三个参与者之间进行分层量子信息拆分的方案。然后我们将该方案推广到任意多量子比特态。分层体现在参与者恢复目标态的不同能力上。高级参与者仅需一个低级参与者的帮助，而低级参与者则需要所有其他参与者的协助。指定接收者执行正算符值测量（POVM），该测量借助哈达玛矩阵精心构建。值得一提的是，推导了恢复操作的一般表达式以揭示其与测量结果的关系。此外，借助簇态的对称性将该方案扩展到多个参与者。
