Trace- and Improved Data-Processing Inequalities for von Neumann Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-09 DOI:10.4171/prims/59-4-1

Stefan Hollands

引用次数: 4

Abstract

We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter et al. on finite dimensional density matrices, yields a bound how well a quantum state can be recovered after it has been passed through a channel. The natural applications of our results are in quantum field theory where the von Neumann algebras are known to be of type III. Along the way we generalize various multi-trace inequalities to general von Neumann algebras.

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冯诺依曼代数的跟踪和改进数据处理不等式

我们证明了一般von Neumann代数的相对熵的数据处理不等式的一个版本，该代数具有涉及测量相对熵的显下界。该不等式推广了Sutter等人之前在有限维密度矩阵上的工作，得出了量子态在通过通道后可以恢复的程度。我们的结果的自然应用是在量子场论，其中冯·诺伊曼代数是已知的III型。在此过程中，我们将各种多迹不等式推广到一般的冯·诺依曼代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.