AI 中文总结
研究连续监测非马尔可夫量子系统中参数估计问题，提出基于反应坐标映射的方法，针对特定线性系统，分析贝叶斯估计，给出费舍尔信息表达式与估计精度缩放，通过玻色子浴温度测量示例证明方法有效性。
AI 中文摘要
连续监测是分析量子系统的有力工具，在量子计量学中作为无损技术被越来越多地使用。通过连续监测获取的噪声数据可用于精确确定系统未知参数。然而，将连接这些数据与基础参数的理论框架扩展到马尔可夫动力学之外非常困难，主要是因为这种动力学不能表示为完全正定可分映射。为克服此问题，我们提出基于反应坐标映射的方法，将这些参数估计技术扩展到马尔可夫区域之外。我们的方法专门针对具有非马尔可夫动力学且经历高斯连续测量（如同调检测）的线性系统。在此框架内，我们分析贝叶斯估计并给出费舍尔信息的解析表达式以及任意参数估计精度的渐近缩放。最后，我们通过玻色子浴温度测量示例证明了我们方法的有效性。
英文摘要
Continuous monitoring is a powerful tool for analyzing quantum systems and is increasingly used as a non-demolition technique in quantum metrology. In this context, noisy data acquired through continuous monitoring can be used to precisely pinpoint unknown parameters of the system. However, extending the theoretical framework that connects these data to the underlying parameters beyond Markovian dynamics is notoriously difficult, primarily because such dynamics cannot be expressed as completely positive divisible maps. To overcome this, we propose a method based on the reaction coordinate mapping to extend these parameter-estimation techniques beyond the Markovian regime. Our approach specifically targets linear systems with non-Markovian dynamics undergoing Gaussian continuous measurements, such as homodyne detection. Within this framework, we analyze Bayesian estimation and provide an analytical expression for the Fisher information, alongside the asymptotic scaling of the estimation precision for arbitrary parameters. Finally, we demonstrate the efficacy of our method through the example of thermometry of a bosonic bath.
Comments7+15 pages, 3 figures
