具有有限维近似性质的量子态
On quantum states with a finite-dimensional approximation property
摘要：
本文考虑一类包含所有有限秩态和无限秩态的量子态的凸集，它们的特征值具有足够的下降率（特别是所有高斯态）。这类量子态的特征在于允许获得关于量子系统和信道的基本熵和信息特性的有限维近似的几个结果的性质（称为FA性质）。我们得到了FA-性质的一个简单的充分条件。我们证明了这一性质蕴涵了冯诺伊曼熵的有限性，但没有解决关于逆蕴涵的问题。我们得到一致的近似结果的特性取决于一对（通道，输入状态）和特性取决于一对（通道，输入合奏）。我们建立了一致的连续性，上述特性的功能的通道w.r.t.强收敛提供了FA性质对于输入态或输入系综的平均态都成立。
英文摘要：
We consider a class (convex set) of quantum states containing all finite rank states and infinite rank states with the sufficient rate of decreasing of eigenvalues (in particular, all Gaussian states). Quantum states from this class are characterized by the property (called the FA-property) that allows to obtain several results concerning finite-dimensional approximation of basic entropic and information characteristics of quantum systems and channels. We obtain a simple sufficient condition of the FA-property. We show that this property implies finiteness of the von Neumann entropy, but leave unsolved the question concerning the converse implication. We obtain uniform approximation results for characteristics depending on a pair (channel, input state) and for characteristics depending on a pair (channel, input ensemble). We establish the uniform continuity of the above characteristics as functions of a channel w.r.t. the strong convergence provided that the FA-property holds either for the input state or for the average state of input ensemble.
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