相干态与贝叶斯对偶
Coherent States and Bayesian Duality
摘要：
我们演示了如何大类的离散和连续的统计分布可以纳入相干态，使用再生核希尔伯特空间的概念。每个家庭的相干态包含，在一种对偶性，这类似于一个类似的贝叶斯统计的对偶性，一个离散的概率分布和一个离散参数化的家庭的连续分布。事实证明，从这个角度来看，在量子光学中广泛研究的非线性相干态是一类特别有用的相干态，因为它们包含许多标准的统计分布。我们还着眼于矢量相干态和多维相干态的混合物的概率分布和联合概率分布的载体。
英文摘要：
We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in a sort of duality, which resembles an analogous duality in Bayesian statistics, a discrete probability distribution and a discretely parametrized family of continuous distributions. It turns out that nonlinear coherent states, of the type widely studied in quantum optics, are a particularly useful class of coherent states from this point of view, in that they contain many of the standard statistical distributions. We also look at vector coherent states and multidimensional coherent states as carriers of mixtures of probability distributions and joint probability distributions.
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