Information Security and National Computing Grid Laboratory, School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China; CSNMT, International Cooperation Research Center of China, Southwest Jiaotong University, Chengdu 610031, China; and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev Lett. 2018 Apr 6;120(14):140402. doi: 10.1103/PhysRevLett.120.140402.
The correlations in quantum networks have attracted strong interest with new types of violations of the locality. The standard Bell inequalities cannot characterize the multipartite correlations that are generated by multiple sources. The main problem is that no computationally efficient method is available for constructing useful Bell inequalities for general quantum networks. In this work, we show a significant improvement by presenting new, explicit Bell-type inequalities for general networks including cyclic networks. These nonlinear inequalities are related to the matching problem of an equivalent unweighted bipartite graph that allows constructing a polynomial-time algorithm. For the quantum resources consisting of bipartite entangled pure states and generalized Greenberger-Horne-Zeilinger (GHZ) states, we prove the generic nonmultilocality of quantum networks with multiple independent observers using new Bell inequalities. The violations are maximal with respect to the presented Tsirelson's bound for Einstein-Podolsky-Rosen states and GHZ states. Moreover, these violations hold for Werner states or some general noisy states. Our results suggest that the presented Bell inequalities can be used to characterize experimental quantum networks.
量子网络中的相关性引起了人们的极大兴趣，因为它们产生了新型的非定域性违背。标准的贝尔不等式无法描述由多个源产生的多体相关性。主要问题是，对于一般的量子网络，没有计算效率高的方法来构造有用的贝尔不等式。在这项工作中，我们通过提出新的、显式的贝尔型不等式，对包括循环网络在内的一般网络进行了显著的改进。这些非线性不等式与等价无权重二分图的匹配问题有关，这允许构建一个多项式时间算法。对于由二体纠缠纯态和广义格林伯格-霍恩-泽林格（GHZ）态组成的量子资源，我们使用新的贝尔不等式证明了具有多个独立观测者的量子网络的一般非定域性。对于爱因斯坦-波多尔斯基-罗森态和 GHZ 态，违反程度相对于 Tsirelson 边界达到最大。此外，这些违反对于 Werner 态或一些一般的噪声态也成立。我们的结果表明，所提出的贝尔不等式可用于描述实验量子网络。
