Universal bound on the eigenvalues of 2-positive trace-preserving maps

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2026-02-01 Epub Date: 2025-10-24 DOI:10.1016/j.laa.2025.10.022

Frederik vom Ende , Dariusz Chruściński , Gen Kimura , Paolo Muratore-Ginanneschi

引用次数: 0

Abstract

We prove an upper bound on the trace of any 2-positive, trace-preserving map in terms of its smallest eigenvalue. We show that this spectral bound is tight, and that 2-positivity is necessary for this inequality to hold in general. Moreover, we use this to infer a similar bound for generators of one-parameter semigroups of 2-positive trace-preserving maps. With this approach we generalize known results for completely positive trace-preserving dynamics while providing a significantly simpler proof that is entirely algebraic.

查看原文本刊更多论文

2-正保持迹映射特征值的全称界

我们用最小特征值证明了任意2正、保迹映射的迹的上界。我们证明了这个谱界是紧的，并且2正性对于这个不等式一般成立是必要的。此外，我们还利用这一理论推导出了2正迹保持映射的单参数半群的生成器的类似界。用这种方法，我们推广了已知的完全正迹保持动力学的结果，同时提供了一个明显更简单的证明，这是完全代数的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.