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arXiv quant-ph/9807008quant-ph
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量子信息理论的语言

Languages of Quantum Information Theory

Andreas Winter

摘要:

本文将介绍量子系统中信息论量的一些符号和定义,如(条件)熵和(条件)互信息。我们将使用自然的C*-代数形式主义,结果证明,语言具有全面的二元论:我们可以为(相容的)可观量定义一切,也可以为(相容的)C*-子代数定义一切。这两种方法在量子操作的形式中是统一的,它们通过一个非常令人满意的不等式联系在一起,推广了著名的Holevo界。然后,我们转向通过(离散无记忆)量子信道通信:我们制定的Fano不等式,限制量子多路信道的容量区域,并评论量子广播信道。

英文摘要:

This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra formalism, and it turns out that one has an allover dualism of language: we can define everything for (compatible) observables, but also for (compatible) C*-subalgebras. The two approaches are unified in the formalism of quantum operations, and they are connected by a very satisfying inequality, generalizing the well known Holevo bound. Then we turn to communication via (discrete memoryless) quantum channels: we formulate the Fano inequality, bound the capacity region of quantum multiway channels, and comment on the quantum broadcast channel.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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