Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain.
Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain.
Phys Rev Lett. 2023 Mar 3;130(9):090201. doi: 10.1103/PhysRevLett.130.090201.
The study of nonlocality in scenarios that depart from the bipartite Einstein-Podolsky-Rosen setup is allowing one to uncover many fundamental features of quantum mechanics. Recently, an approach to building network-local models based on machine learning led to the conjecture that the family of quantum triangle distributions of [Renou et al., Phys. Rev. Lett. 123, 140401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.140401] did not admit triangle-local models in a larger range than the original proof. We prove part of this conjecture in the affirmative. Our approach consists of reducing the family of original, four-outcome distributions to families of binary-outcome ones, and then using the inflation technique to prove that these families of binary-outcome distributions do not admit triangle-local models. This constitutes the first successful use of inflation in a proof of quantum nonlocality in networks for distributions whose nonlocality could not be proved with alternative methods. Moreover, we provide a method to extend proofs of network nonlocality in concrete distributions of a parametrized family to continuous ranges of the parameter. In the process, we produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
在偏离双体爱因斯坦-波多尔斯基-罗森设置的场景中研究非局域性，使得人们能够揭示出量子力学的许多基本特征。最近，一种基于机器学习构建网络局域模型的方法导致了这样的猜想，即[Renou 等人，物理评论快报 123, 140401 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.140401]的量子三角形分布族在比原始证明更大的范围内不允许存在三角形局域模型。我们在肯定的方面证明了这个猜想的一部分。我们的方法包括将原始的四进制分布族简化为二进制分布族，然后使用膨胀技术证明这些二进制分布族不允许存在三角形局域模型。这是在网络中使用膨胀技术证明量子非局域性的分布的首次成功应用，这些分布的非局域性无法用其他方法证明。此外，我们提供了一种方法，可以将具体分布族中网络非局域性的证明扩展到参数的连续范围。在这个过程中，我们为具有二进制结果的三角形场景生成了大量的网络贝尔不等式，这些不等式具有独立的兴趣。
