Local State Transition of Feedback Controlled Quantum Systems with Imperfect Detector Efficiency: Part I: Differential Geometric Analysis for Dynamical Systems with Matrix-Valued States
Local State Transition of Feedback Controlled Quantum Systems with Imperfect Detector Efficiency: Part I: Differential Geometric Analysis for Dynamical Systems with Matrix-Valued States
复制标题
具有不完美探测器效率的反馈控制量子系统的局域状态转变：第一部分：具有矩阵值状态的动力系统的微分几何分析
DOI：
10.9746/jcmsi.3.409
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Tsumura
中科院分区：
文献类型：
--
作者：
Tomotake Sasaki;S. Hara;K. Tsumura
我们考虑一类新的动力系统，其状态由厄米特矩阵表示的动机治疗量子控制问题。我们开发的理论和技术的微分几何分析动力系统在这一类，其中李积矩阵函数的介绍，并发挥了重要作用。我们提供了一个简单的和坐标自由的计算方法，使有效的微分几何分析的矩阵函数的李积。本文的结果将被用于后续的论文中的连续量子测量与不完美的检测器效率的受控量子系统的局部状态转移的分析。
We consider a new class of dynamical systems whose state is represented by a Hermitian matrix motivated by treating quantum control problems. We develop theory and techniques of differential geometric analysis for dynamical systems in that class, where a Lie product of matrix functions is introduced and plays an important role. We provide a simple and coordinate-free calculation method for the Lie product of matrix functions which enables efficient differential geometric analysis. The result of this paper will be used in a follow-up paper on analysis of local state transition of controlled quantum systems under continuous quantum measurement with imperfect detector efficiency.