论文标题
简单量子上下文
Simplicial quantum contextuality
论文作者
论文摘要
我们介绍了一个基于简单集，拓扑空间的组合模型的新框架，这些框架在现代同义理论中起着重要作用。我们的方法将测量场景扩展到由测量和结果的空间（而不是集合）组成，从而将非信号分布概括为简单分布，这些分布是通过简单集建模的空间上的分布。使用这种形式主义，我们提出了一种拓扑启发的，这是Fine定理的新证明，用于表征贝尔场景中的非上下文性。强大的上下文是为了简单的分布而适当地将其定义的，从而使我们可以定义的共同体证人将较早的拓扑结构扩展到量子可观察到的代数关系的早期拓扑结构到概率分布的水平。量子理论的基础定理，例如格里森的定理和科钦 - 雪橇定理，可以在这种新语言中自然表达。
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces (rather than sets) of measurements and outcomes, and thereby generalizes nonsignaling distributions to simplicial distributions, which are distributions on spaces modeled by simplicial sets. Using this formalism we present a topologically inspired new proof of Fine's theorem for characterizing noncontextuality in Bell scenarios. Strong contextuality is generalized suitably for simplicial distributions, allowing us to define cohomological witnesses that extend the earlier topological constructions restricted to algebraic relations among quantum observables to the level of probability distributions. Foundational theorems of quantum theory such as the Gleason's theorem and Kochen-Specker theorem can be expressed naturally within this new language.
