Quantum mechanics predicts non-local correlations in spatially extended entangled quantum systems, and these correlations are empirically very well confirmed. This raises philosophical questions of how nature could be that way, prompting the study of purported completions of quantum mechanics by hidden variables. Bell-type theorems connect assumptions about hidden variables with empirical predictions for the outcome of quantum correlation experiments. From among these assumptions, the Setting Independence assumption has received the least formal attention. Its violation is, however, central in the recent discussion about super-deterministic models for quantum correlation experiments. In this paper, we focus on the non-local modal correlations in the GHZ experiment. We model the introduction of hidden variables in the form of instruction sets via structure extensions in the framework of Branching Space-Times. This framework allows us to show in formal detail how the introduction of non-contextual instruction sets results in a specific violation of Setting Independence; a similar result is derived for contextual instruction sets. Our discussion provides additional reasons for foregoing the introduction of local hidden variables, and for accepting non-local quantum correlations as a resource provided by nature.

量子力学预测空间扩展的纠缠量子系统中的非局域相关性，并且这些相关性在经验上得到了很好的证实。这就提出了自然如何会是这样的哲学问题，从而促进了对隐变量所谓的量子力学完成的研究。贝尔型定理将隐变量的假设与量子相关实验结果的经验预测联系起来。在这些假设中，设置独立性假设受到的正式关注最少。然而，它的违反是最近关于量子相关实验的超确定性模型的讨论的核心。在本文中，我们重点研究 GHZ 实验中的非局部模态相关性。我们在分支时空框架中通过结构扩展以指令集的形式引入隐藏变量。这个框架使我们能够正式详细地展示引入非上下文指令集如何导致对设置独立性的特定违反；对于上下文指令集也得出类似的结果。我们的讨论为前面引入局部隐变量以及接受非局部量子相关性作为自然提供的资源提供了额外的理由。