无约束假设下的广义概率论
Generalized Probabilistic Theories Without the No-Restriction Hypothesis
摘要：
广义概率论是研究量子理论物理基础的一种常用方法。标准框架假定无限制假设，其中物理理论的状态空间确定测量集。然而，这种假设并不是出于物理动机。我们概括的框架，占系统不遵守无限制的假设。然后，我们展示了我们的框架可以用来描述新的类的概率理论，例如，其中包括固有噪声。放松限制假设也允许我们引入一个“自对偶”过程，这产生了一类新的理论，它们具有量子理论的许多特征，例如服从Tsirelson的最大纠缠态的界限。然后，我们表征联合状态，推广的最大张量积。我们展示了如何这个新的张量积可以用来描述的凸封闭的Spekkens玩具理论，并在这样做，我们获得了分析，为什么它是本地的几何形状的状态空间。我们表明，无限制版本的Spekkens玩具理论是被称为“盒子世界”的理论，允许最大的非局部相关性。
英文摘要：
The framework of generalized probabilistic theories (GPTs) is a popular approach for studying the physical foundations of quantum theory. The standard framework assumes the no-restriction hypothesis, in which the state space of a physical theory determines the set of measurements. However, this assumption is not physically motivated. We generalize the framework to account for systems that do not obey the no-restriction hypothesis. We then show how our framework can be used to describe new classes of probabilistic theories, for example those which include intrinsic noise. Relaxing the restriction hypothesis also allows us to introduce a 'self-dualization' procedure, which yields a new class of theories that share many features of quantum theory, such as obeying Tsirelson's bound for the maximally entangled state. We then characterize joint states, generalizing the maximal tensor product. We show how this new tensor product can be used to describe the convex closure of the Spekkens toy theory, and in doing so we obtain an analysis of why it is local in terms of the geometry of its state space. We show that the unrestricted version of the Spekkens toy theory is the theory known as 'boxworld' that allows maximal nonlocal correlations.
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