POVM的Kolmogorov扩张定理
A Kolmogorov Extension Theorem for POVMs
摘要：
我们证明了一个关于正算子值测度（POVMs）的定理，它类似于概率论的标准定理Kolmogorov扩张定理。根据我们的定理，如果$\mathbb{R}^n$上的POVM序列G_n满足相容性（或投射性）条件$G_{n+1}(A\times \mathbb{R}) = G_n(A)$，则在无限序列空间$\mathbb{R}^\mathbb{N}$上存在一个POVM G，它的前n个元素以G_n为边界.我们还描述了在量子理论中的应用。
英文摘要：
We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem, a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G_n on $\mathbb{R}^n$ satisfies the consistency (or projectivity) condition $G_{n+1}(A\times \mathbb{R}) = G_n(A)$ then there is a POVM G on the space $\mathbb{R}^\mathbb{N}$ of infinite sequences that has G_n as its marginal for the first n entries of the sequence. We also describe an application in quantum theory.
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