Continuous-time measurements are instrumental for a multitude of tasks in quantum engineering and quantum control, including the estimation of dynamical parameters of open quantum systems monitored through the environment. However, such measurements do not extract the maximum amount of information available in the output state, so finding alternative optimal measurement strategies is a major open problem. In this paper we solve this problem in the setting of discrete-time input-output quantum Markov chains. We present an efficient algorithm for optimal estimation of one-dimensional dynamical parameters which consists of an iterative procedure for updating a `measurement filter' operator and determining successive measurement bases for the output units. A key ingredient of the scheme is the use of a coherent quantum absorber as a way to post-process the output after the interaction with the system. This is designed adaptively such that the joint system and absorber stationary state is pure at a reference parameter value. The scheme offers an exciting prospect for optimal continuous-time adaptive measurements, but more work is needed to find realistic practical implementations.

翻译：连续时间测量在量子工程和量子控制中的众多任务中起着重要作用，包括通过环境监测的开放量子系统的动力学参数估计。然而，这类测量并未从输出状态中提取最大可用信息量，因此寻找替代的最优测量策略是一个重要的开放性问题。本文在离散时间输入-输出量子马尔可夫链的框架下解决了该问题。我们提出了一种高效算法，用于一维动力学参数的最优估计，该算法包含一个迭代过程，用于更新"测量滤波器"算子并确定输出单元的连续测量基。该方案的关键要素是使用相干量子吸收体，作为系统相互作用后对输出进行后处理的手段。通过自适应设计，使联合系统与吸收体在参考参数值下的稳态保持纯态。该方案为连续时间自适应测量提供了令人振奋的前景，但实现现实可行的实际应用仍需进一步研究。