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的多项任务中具有重要作用，包括通过环境监测开放量子系统的动力学参数估计。然而，这类测量无法从输出态中提取最大可用信息量，因此寻找替代的最优测量策略仍是一个重大未解问题。本文在离散时间输入-输出量子马尔可夫链框架下解决了该问题。我们提出了针对一维动力学参数最优估计的高效算法，该算法通过迭代更新“测量滤波器”算子并确定输出单元的连续测量基来实现。该方案的核心在于利用相干量子吸收器在系统相互作用后对输出进行后处理，该吸收器被自适应地设计，使得在参考参数值下联合系统与吸收器稳态保持纯态。该方案为最优连续时间自适应测量提供了令人振奋的前景，但仍需进一步探索实现现实可行的实践方案。