A strong subadditivity-like inequality for quantum entropy in semifinite von Neumann algebras

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-06-04 DOI:10.1002/mana.202300383

Andrzej Łuczak

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引用次数: 0

Abstract

Let $M$ be a semifinite von Neumann algebra with a normal faithful semifinite trace $τ$ , and let $A$ , $B$ , $R$ be its subalgebras such that $R \subset A \cap B$ and that $τ$ restricted to any of these subalgebras is semifinite. Denote by $E_{A}$ , $E_{B}$ , and $E_{R}$ the normal conditional expectations from $M$ onto $A$ , $B$ and $R$ , respectively, such that $τ$ is invariant with respect to any of them. The quadruple $M$ , $A$ , $B$ , $R$ is said to be a commuting square if

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半有限冯-诺依曼代数中量子熵的强次熵不等式

设是一个半有穷冯-诺依曼代数，有一个正则忠实半有穷迹线 , 并设 , , 是它的子代数，使得和限于其中任何一个子代数都是半有穷的。用 , , 和分别表示来自于 , 和 , 的正态条件期望，使得相对于它们中的任何一个都是不变的。我们还研究了上述不等式中相等的情况，并得到了各种等价条件，其中有限冯-诺依曼代数方程的形式尤其吸引人。对于这类数组，在数组和的独立性假设下，还可以得到一个条件 .

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index