框架希尔伯特空间：悬挂量子理论的准概率图像
Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
摘要：
在早期工作的基础上，我们进一步发展了一种基于框架的数学理论的形式主义，该框架定义了有限维量子系统的一组可能的相空间或准概率表示。我们证明了另一种方法来定义一组准概率表示，基于一个更自然的推广的经典表示，是等价于我们以前的方法基于框架，因此也受到我们的不去定理的非负表示。此外，我们澄清了量子理论的上下文性和准概率表示中否定性的必要性之间的关系，并讨论了它们作为非经典性标准的相关性。我们还提供了一个全面的概述已知的准概率表示和他们的表达框架内的形式主义。
英文摘要：
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an alternate approach to defining a set of quasi-probability representations, based on a more natural generalization of a classical representation, is equivalent to our earlier approach based on frames, and therefore is also subject to our no-go theorem for a non-negative representation. Furthermore, we clarify the relationship between the contextuality of quantum theory and the necessity of negativity in quasi-probability representations and discuss their relevance as criteria for non-classicality. We also provide a comprehensive overview of known quasi-probability representations and their expression within the frame formalism.
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