论文标题
关于使用状态分解进行减少动态的研究
On the use of total state decompositions for the study of reduced dynamics
论文作者
论文摘要
在与环境之间存在初始相关性的情况下，开放量子系统动力学的描述需要与减少动力学的标准方法不同的数学工具，这是基于使用时间依赖的完全正面痕迹保留（CPTP）映射的。在这里，我们考虑了一种基于任何可能相关的二分状状态的分解方法，该方法是涉及统计运算符的圆锥组合，将统计运算符和系统上的一般线性运算符在系统上，这允许人们通过一组有限的时间相关的CPTP映射来固定减少系统的演变。特别是，我们表明这种分解始终存在，也存在于无限的尺寸希尔伯特空间，并且所产生的CPTP映射的数量受初始全局状态的Schmidt等级的界定。我们进一步调查了CPTP地图是Gorini-Kossakowski-Lindblad-Sudarshan形式的发电机的半群的情况；对于两个简单的Qubit模型，我们确定由CPTP Semogroup固定的任何演化时间的初始状态定义的阳性域。
The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a time-dependent completely positive trace preserving (CPTP) map. Here, we take into account an approach that is based on a decomposition of any possibly correlated bipartite state as a conical combination involving statistical operators on the environment and general linear operators on the system, which allows one to fix the reduced-system evolution via a finite set of time-dependent CPTP maps. In particular, we show that such a decomposition always exists, also for infinite dimensional Hilbert spaces, and that the number of resulting CPTP maps is bounded by the Schmidt rank of the initial global state. We further investigate the case where the CPTP maps are semigroups with generators in the Gorini-Kossakowski-Lindblad-Sudarshan form; for two simple qubit models, we identify the positivity domain defined by the initial states that are mapped into proper states at any time of the evolution fixed by the CPTP semigroups.
