论文标题
关于量子自旋1/2系统稳定反馈的鲁棒性
On the robustness of stabilizing feedbacks for quantum spin-1/2 systems
论文作者
论文摘要
在本文中，我们考虑了描述与经过连续时间测量的电磁场相互作用的量子自旋1/2系统演变的随机主方程。我们假设初始状态和物理参数的确切值未知。我们证明[16]中考虑的反馈稳定策略对这些不完美是可靠的。通过研究耦合随机主方程的渐近行为，这些方程描述了实际状态的演变以及在反馈控制器的适当假设下估计的渐变行为。我们为反馈控制器和估计参数的有效域提供了足够的条件，这些域确保了耦合系统的指数稳定。此外，我们的结果使我们能够在具有未知初始状态的SPIN-1/2系统的情况下对[15，猜想4.4]进行积极回答，即使在存在不当已知的物理参数的情况下也是如此。
In this paper, we consider stochastic master equations describing the evolution of quantum spin-1/2 systems interacting with electromagnetic fields undergoing continuous-time measurements. We suppose that the initial states and the exact values of the physical parameters are unknown. We prove that the feedback stabilization strategy considered in [16] is robust to these imperfections. This is shown by studying the asymptotic behavior of the coupled stochastic master equations describing the evolutions of the actual state and the estimated one under appropriate assumptions on the feedback controller. We provide sufficient conditions on the feedback controller and a valid domain of estimated parameters which ensure exponential stabilization of the coupled system. Furthermore, our results allow us to answer positively to [15,Conjecture 4.4] in the case of spin-1/2 systems with unknown initial states, even in presence of imprecisely known physical parameters.
