论文标题
N级量子自旋系统的强大反馈稳定
Robust feedback stabilization of N-level quantum spin systems
论文作者
论文摘要
在本文中，我们认为N级量子角动量系统与经过连续时间测量的电磁场相互作用。我们假设对初始状态和物理参数的不认识，需要引入代表估计量子状态的附加状态。量子态的演变及其估计是通过耦合随机主方程来描述的。在这里，我们研究了在反馈控制器存在下这种系统的渐近行为。我们在反馈控制器和估计参数上提供足够的条件，以确保耦合随机系统向测量算子的特征状态的指数稳定。此外，我们估计收敛速率。我们还提供满足此类条件的参数反馈定律。我们的结果表明，在估计状态的初始化不精确并在未知的物理参数方面，反馈稳定策略的鲁棒性。
In this paper, we consider N-level quantum angular momentum systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose unawareness of the initial state and physical parameters, entailing the introduction of an additional state representing the estimated quantum state. The evolution of the quantum state and its estimation is described by a coupled stochastic master equation. Here, we study the asymptotic behavior of such a system in presence of a feedback controller. We provide sufficient conditions on the feedback controller and on the estimated parameters that guarantee exponential stabilization of the coupled stochastic system towards an eigenstate of the measurement operator. Furthermore, we estimate the corresponding rate of convergence. We also provide parametrized feedback laws satisfying such conditions. Our results show the robustness of the feedback stabilization strategy considered in [21] in case of imprecise initialization of the estimated state and with respect to the unknown physical parameters.
