标题： 跳跃扩散随机主方程的参数估计 显示英文标题

标题： Parameter Estimation for Jump-Diffusion Stochastic Master Equations

摘要： 本文研究在连续观测下开放量子系统的参数估计，其条件动力学由与量子非破坏性（QND）测量相关的跳跃扩散随机主方程（SMEs）所支配。 诸如耦合强度或测量效率之类的模型参数的估计是必不可少的，但在实际中这些参数通常是不确定的。 我们首先建立了约化量子滤波器的存在性和适定性：对于N级系统，条件演化可以表示为O(N)维实状态空间，而不是完整的O(N^2)密度矩阵状态空间。 在此基础上，我们扩展了量子滤波器的稳定性理论，表明指数收敛不仅在初始状态不匹配的情况下持续存在，而且在参数不匹配的情况下也保持。 最后，我们开发了一个连续参数域的估计框架，并证明了在长时间极限下估计量的几乎必然一致性。 这些结果为跳跃扩散SMEs的参数估计提供了严格的处理方法，结合了结构约化与稳定性和可辨识性分析，从而扩展了开放量子系统参数估计的数学理论。 显示英文摘要

摘要： This paper investigates parameter estimation for open quantum systems under continuous observation, whose conditional dynamics are governed by jump-diffusion stochastic master equations (SMEs) associated with quantum nondemolition (QND) measurements. Estimation of model parameters such as coupling strengths or measurement efficiencies is essential, yet in practice these parameters are often uncertain. We first establish the existence and well-posedness of a reduced quantum filter: for an N-level system, the conditional evolution can be represented in an O(N)-dimensional real state space rather than the full O(N^2) density-matrix state space. Building on this, we extend the stability theory of quantum filters, showing that exponential convergence persists not only under mismatched initial states but also in the presence of parameter mismatch. Finally, we develop an estimation framework for continuous parameter domains and prove almost sure consistency of the estimator in the long-time limit. These results yield a rigorous treatment of parameter estimation for jump-diffusion SMEs, combining structural reduction with stability and identifiability analysis, and thereby extend the mathematical theory of parameter estimation for open quantum systems.