Abstract

We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed under concatenations and tensor products. We obtain asymptotically tight universal continuity bounds for the output entropy of two types of quantum channels: channels with finite output entropy and energy-constrained channels preserving finiteness of the entropy.

中文翻译：

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冯·诺依曼熵的量子通道和保有限性

摘要

我们描述了将有限熵的状态映射为有限熵的状态的量子通道的类（半群）。我们特别表明，该类自然分解为三个凸子类，其中两个在子级数和张量积下是封闭的。对于两种类型的量子通道的输出熵，我们获得了渐近紧的通用连续性界：具有有限输出熵的通道和保持熵的有限性的能量受限通道。