无限维动态映射的可整除性

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2026-05-01 Epub Date: 2026-01-20 DOI:10.1016/j.laa.2026.01.020

Bihalan Bhattacharya , Uwe Franz , Saikat Patra , Ritabrata Sengupta

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引用次数: 0

摘要

完全正迹保持映射在量子信息理论中有着广泛的应用。这些大多是用主方程的角度来研究的。这个理论的中心部分是研究一个给定的动态映射系统{Λt:t≥0}是马尔可夫的还是非马尔可夫的。我们研究了底层希尔伯特空间为无限维时的问题。构造了检验P (r)的充分条件。动态映射的可整除性。我们构造了几个例子，其中潜在的希尔伯特空间可能不是有限维的。我们还特别强调了高斯动态映射，并在其中得到了一个版本的结果。

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Divisibility of infinite dimensional dynamical maps

Completely positive trace preserving maps are widely used in quantum information theory. These are mostly studied using the master equation perspective. A central part in this theory is to study whether a given system of dynamical maps

{Λ_{t} : t \geq 0}

is Markovian or non-Markovian. We study the problem when the underlying Hilbert space is of infinite dimension. We construct a sufficient condition for checking P (resp. CP) divisibility of dynamical maps. We construct several examples where the underlying Hilbert space may not be of finite dimension. We also give a special emphasis on Gaussian dynamical maps and get a version of our result in it.

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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.