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arXiv 2204.06648quant-phmath.AT
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单纯量子上下文性

Simplicial quantum contextuality

Cihan Okay, Aziz Kharoof, Selman Ipek

AI总结:

本文提出基于单纯集的量子上下文性新框架,将测量场景扩展至空间并推广非信号分布为单纯分布,利用上同调见证将拓扑构造扩展至概率分布层面,并自然表达Fine、Gleason及Kochen-Specker等基础定理。

摘要:

我们引入了一个基于单纯集的上下文性新框架,单纯集是拓扑空间的组合模型,在现代同伦理论中发挥着重要作用。我们的方法将测量场景扩展为由测量的空间(而非集合)和结果组成,从而将非信号分布推广为单纯分布,即在由单纯集建模的空间上的分布。利用这一形式体系,我们给出了一个受拓扑启发的 Fine 定理新证明,用于表征 Bell 场景中的非上下文性。强上下文性被适当地推广到单纯分布,使我们能够定义上同调见证,将先前局限于量子可观测量代数关系的拓扑构造扩展到概率分布层面。量子理论的基础定理,如 Gleason 定理和 Kochen-Specker 定理,可以在这一新语言中自然地表达。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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