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众多任务中至关重要,包括通过环境监测开放量子系统的动态参数估计。然而,这些测量并未提取输出状态中可用的最大信息量,因此寻找其他最优测量策略是一个重大的开放性问题。在本文中,我们在离散时间输入输出量子马尔科夫链的环境下解决了这个问题。我们提出了一种高效的算法,用于最优一维动态参数估计,该算法包括一个用于更新“测量滤波器”算子和确定输出单元的连续测量基的迭代过程。该方案的关键组成部分是使用相干量子吸收器作为和系统交互后输出的后处理方式。该吸收器的自适应设计是这样的,在参考参数值处联合系统和吸收器的定态为纯态。该方案为最优连续时间自适应测量提供了迷人的前景,但需要更多的工作来找到实际可行的实现。