论文标题
量子finetti定理是分类限制，以及c* - 代理的状态空间的限制
Quantum de Finetti Theorems as Categorical Limits, and Limits of State Spaces of C*-algebras
论文作者
论文摘要
de finetti定理告诉我们，如果我们期望结果的可能性独立于其顺序，那么这些结果序列可以通过从分布中随机绘制实验并反复重复的结果来产生这些结果序列。特别是，量子finetti定理说，量子状态的可交换序列总是由一遍又一遍地产生的单个状态的分布表示。本文的主要结果是，这种量子finetti结构具有普遍的特性，这是一个分类的限制。这使我们能够在有限维量子理论的分类处理和无限维度之间通过典型地通过。这里的处理是通过了解（CO）限制的违反功能子的特性，该函数采用了C*-Algebra，将物理系统描述到其凸面，紧凑的状态空间，以及通过讨论RADON概率单月。我们还表明，相同的分类分析也证明了经典概率的连续DE Finetti定理合理。
De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and repeating it over and over. In particular, the quantum de Finetti theorem says that exchangeable sequences of quantum states are always represented by distributions over a single state produced over and over. The main result of this paper is that this quantum de Finetti construction has a universal property as a categorical limit. This allows us to pass canonically between categorical treatments of finite dimensional quantum theory and the infinite dimensional. The treatment here is through understanding properties of (co)limits with respect to the contravariant functor which takes a C*-algebra describing a physical system to its convex, compact space of states, and through discussion of the Radon probability monad. We also show that the same categorical analysis also justifies a continuous de Finetti theorem for classical probability.
