Bell non-locality and Kochen–Specker (KS) contextuality are logically independent concepts, fuel different protocols with quantum vs classical advantage, and have distinct classical simulation costs. A natural question is what are the relations between these concepts, advantages, and costs. To address this question, it is useful to have a map that captures all the connections between Bell non-locality and KS contextuality in quantum theory. The aim of this work is to introduce such a map. After defining the theory-independent notions of Bell non-locality and KS contextuality for ideal measurements, we show that, in quantum theory, due to Neumark’s dilation theorem, every quantum Bell non-local behavior can be mapped to a formally identical KS contextual behavior produced in a scenario with identical relations of compatibility but where measurements are ideal and no space-like separation is required. A more difficult problem is identifying connections in the opposite direction. We show that there are “one-to-one” and partial connections between KS contextual behaviors and Bell non-local behaviors for some KS scenarios, but not for all of them. However, there is also a method that transforms any KS contextual behavior for quantum systems of dimension d into a Bell non-local behavior between two quantum subsystems each of them of dimension d. We collect all these connections in map and list some problems which can benefit from this map.

贝尔非本地性和Kochen-Specker（KS）上下文是逻辑上独立的概念，它们在量子和经典优势之间助长了不同的协议，并且具有明显的经典模拟成本。一个自然的问题是这些概念，优势和成本之间的关系是什么。为了解决这个问题，有一个映射图可以捕获量子理论中贝尔非局部性和KS上下文之间的所有联系。这项工作的目的是介绍这样的地图。在定义了理想测量的Bell非局部性和KS上下文无关的理论独立概念后，我们证明，在量子理论中，由于Neumark的扩张定理，每个量子钟的非局部行为都可以映射到在具有相同兼容性关系的场景中产生的形式完全相同的KS上下文行为，但是在这种情况下，测量是理想的，并且不需要像空间一样的分隔。一个更困难的问题是确定相反方向的连接。我们显示，对于某些KS场景，但并非对于所有KS场景，KS上下文行为与Bell非本地行为之间存在“一对一”和部分连接。但是，还有一种方法可以转换尺寸量子系统的任何KS上下文行为 我们显示，对于某些KS场景，但并非对于所有KS场景，KS上下文行为与Bell非本地行为之间存在“一对一”和部分连接。但是，还有一种方法可以转换尺寸量子系统的任何KS上下文行为 我们显示，对于某些KS场景，但并非对于所有KS场景，KS上下文行为与Bell非本地行为之间存在“一对一”和部分连接。但是，还有一种方法可以转换尺寸量子系统的任何KS上下文行为d变成两个量子子系统，每个子系统的维数为d的Bell非局部行为。我们在地图中收集了所有这些连接，并列出了一些可以从该地图中受益的问题。