g循环量子马尔可夫半群

IF 1.3 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Open Systems & Information Dynamics Pub Date : 2023-03-01 DOI:10.1142/s1230161223500026

J. R. Bolaños-Servín, R. Quezada, Josué Vázquez-Becerra

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引用次数: 0

摘要

我们拓宽了循环量子马尔可夫半群的研究。首先，我们将[公式:见文]-循环GKSL生成器和[公式:见文]-循环QMS的概念从对应于[公式:见文]的循环情况引入到任意有限群[公式:见文]。其次，我们证明了每个[公式:见文]-循环GKSL生成器具有块对角线表示[公式:见文]，其中[公式:见文]是由一些[公式:见文]确定的[公式:见文]-循环矩阵。用[公式:见文]支持下生成的[公式:见文]子群[公式:见文]表示[公式:见文]，证明[公式:见文]有自己的块对角矩阵表示[公式:见文]，其中[公式:见文]是一个不可约的[公式:见文]-循环矩阵，[公式:见文]是[公式:见文]中[公式:见文]的索引。最后，我们利用这样的块表示来表征循环qms的结构、稳态和渐近演化[公式:见文本]。

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G-Circulant Quantum Markov Semigroups

We broaden the study of circulant Quantum Markov Semigroups (QMS). First, we introduce the notions of [Formula: see text]-circulant GKSL generator and [Formula: see text]-circulant QMS from the circulant case, corresponding to [Formula: see text], to an arbitrary finite group [Formula: see text]. Second, we show that each [Formula: see text]-circulant GKSL generator has a block-diagonal representation [Formula: see text], where [Formula: see text] is a [Formula: see text]-circulant matrix determined by some [Formula: see text]. Denoting by [Formula: see text] the subgroup of [Formula: see text] generated by the support of [Formula: see text], we prove that [Formula: see text] has its own block-diagonal matrix representation [Formula: see text] where [Formula: see text] is an irreducible [Formula: see text]-circulant matrix and [Formula: see text] is the index of [Formula: see text] in [Formula: see text]. Finally, we exploit such block representations to characterize the structure, steady states, and asymptotic evolution of [Formula: see text]-circulant QMSs.

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来源期刊

Open Systems & Information Dynamics 工程技术-计算机：信息系统

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Journal is to promote interdisciplinary research in mathematics, physics, engineering and life sciences centered around the issues of broadly understood information processing, storage and transmission, in both quantum and classical settings. Our special interest lies in the information-theoretic approach to phenomena dealing with dynamics and thermodynamics, control, communication, filtering, memory and cooperative behaviour, etc., in open complex systems.