Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured. Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network. Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.
翻译:Bell 的理论通常被理解为量子理论与本地隐藏的可变模型不相容的证据。 更一般地说,我们可以看到,违反Bell 不平等的情况证明不可能解释与古典因果模型的量子相关关系。 然而,违反Bell 不平等的情况并不排除允许某种程度的衡量依赖的经典模式,即观察员所作的选择可以与生成系统的来源相关联。在这里,我们表明,如果我们在网络中安排Bell 测试,衡量依赖程度在数量上可以达到最高界限。此外,我们还证明,这些结果可以调整,以便为一大批因果网络产生非线性Bell不平等,并查明违反这些不平等的可数量上可实现的关联。