概率分布和密度算子源的压缩
Compression of sources of probability distributions and density operators
摘要：
我们研究的问题的有效压缩的随机源的概率分布。它可以被看作是香农信源编码问题的推广。它与公共随机性理论、信道编码和率失真理论有关：在前两个主题中，我们可以导出已建立的编码定理的“逆”，从而得到证明逆定理的一种新方法;在第三个主题中，我们找到Shannon率失真定理的一种新证明。在回顾了已知的最佳压缩率的下限，我们提出了一些方法来实现它的代码结构。我们的主要结果是：更好地理解已知的压缩率的下限通过一个强版本的这一声明，审查建设实现下限通过使用共同的随机性，我们补充显示最佳使用后者在一类协议。然后，我们回顾了另一种方法，不依赖于共同的随机性，以最大限度地减少压缩率，提供了一些洞察其组合结构，并提出了一种算法来优化it. The第二部分的文件是关注的问题的推广到量子信息理论：混合量子态的压缩。在这里，在回顾了已知的下限后，我们贡献了一个强版本，并讨论了这个问题与量子信息理论中其他问题的关系。
英文摘要：
We study the problem of efficient compression of a stochastic source of probability distributions. It can be viewed as a generalization of Shannon's source coding problem. It has relation to the theory of common randomness, as well as to channel coding and rate--distortion theory: in the first two subjects ``inverses'' to established coding theorems can be derived, yielding a new approach to proving converse theorems, in the third we find a new proof of Shannon's rate--distortion theorem. After reviewing the known lower bound for the optimal compression rate, we present a number of approaches to achieve it by code constructions. Our main results are: a better understanding of the known lower bounds on the compression rate by means of a strong version of this statement, a review of a construction achieving the lower bound by using common randomness which we complement by showing the optimal use of the latter within a class of protocols. Then we review another approach, not dependent on common randomness, to minimizing the compression rate, providing some insight into its combinatorial structure, and suggesting an algorithm to optimize it. The second part of the paper is concerned with the generalization of the problem to quantum information theory: the compression of mixed quantum states. Here, after reviewing the known lower bound we contribute a strong version of it, and discuss the relation of the problem to other issues in quantum information theory.
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