A note on the infinite-dimensional quantum Strassen’s theorem

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2022-04-18 DOI:10.1142/s0219025722500060

L. Accardi, Abdallah Dhahri, Y. Lu

引用次数: 0

Abstract

In Ref. [3], the quantum Strassen’s theorem has been extended to the infinite-dimensional case. This theorem consists in the solution of the coupling problem for two states on the algebra of bounded operators on two Hilbert spaces [Formula: see text], [Formula: see text] with the additional constraint that the coupling state has support in a pre-assigned sub-space of [Formula: see text]. In this paper, we give an alternative proof of the main theorem in Ref. [3] that allows such extension.

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关于无限维量子Strassen定理的注解

在文献[3]中，量子Strassen定理已推广到无限维情况。该定理包含两个Hilbert空间[公式:见文]，[公式:见文]上有界算子代数上两个状态耦合问题的解，附加约束是耦合状态在[公式:见文]的一个预先分配的子空间中得到支持。在本文中，我们给出了文献[3]中允许这种扩展的主要定理的另一种证明。

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

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.