北京邮电大学Fei Gao团队表征了制备和测量量子多链状网络中的量子关联集。这一研究成果于2025年2月24日发表在《物理评论A》杂志上。

研究组引入了一个由任何概率分布满足的测试层次结构，该概率分布P表示在制备和测量（P&M）量子多链形网络中生成的量子相关性，仅假设制备态的内积信息。P&M量子多链网络涉及多个测量方，每个测量方都可能有多个连续的接收器。通过引入有限数量的线性和正半定约束来表征P&M量子多链网络中的量子关联，从而调整了原始的Navascués、Pironio和Acín（NPA）层次结构。

每个层次中的这些约束都是从顺序测量和准备状态的内积矩阵中推导得出。改进的NPA层次结构进一步应用于处理一些量子信息任务，包括顺序量子随机访问码（QRAC）和半设备无关随机性认证。首先，他们推导了2→1顺序QRAC中两个顺序接收器之间的最优权衡，并研究了其双重违规区域中的随机性证明。其次，考虑到实际通信中存在窃听者，又展示了使用2→1个连续QRAC的最佳权衡可以证明多少局部和全局随机性。最后，还量化了可以从两个连续接收器生成的完整概率集中证明的局部和全局随机性。

研究组得出结论，利用全组概率比仅依赖最优权衡关系证明了更多的随机性。

附：英文原文

Title: Characterizing the set of quantum correlations in prepare-and-measure quantum multichain-shaped networks

Author: Yanning Jia, Fenzhuo Guo, Yukun Wang, Haifeng Dong, Fei Gao

Issue&Volume: 2025/02/24

Abstract: We introduce a hierarchy of tests satisfied by any probability distribution P that represents the quantum correlations generated in prepare-and-measure (P&M) quantum multichain-shaped networks, assuming only the inner-product information of prepared states. The P&M quantum multichain-shaped networks involve multiple measurement parties, with each measurement party potentially having multiple sequential receivers. We adapt the original Navascués, Pironio, and Acín (NPA) hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P&M quantum multichain-shaped networks. These constraints in each hierarchy are derived from sequential measurements and the inner-product matrix of prepared states. The adapted NPA hierarchy is further applied to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and semi-device-independent randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the 2→1 sequential QRACs, and investigate randomness certification in its double violation region. Second, considering the presence of an eavesdropper in actual communication, we show how much local and global randomness can be certified using the optimal trade-off of 2→1 sequential QRACs. We also quantify the amount of local and global randomness that can be certified from the complete set of probabilities generated by the two sequential receivers. Our conclusion is that utilizing the full set of probabilities certifies more randomness than relying solely on the optimal trade-off relationship.

DOI: 10.1103/PhysRevA.111.022439

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.022439