We analyze the estimation of a time-dependent perturbation acting on a continuously monitored quantum system. We describe the temporal fluctuations of the perturbation by a hidden Markov model, and we combine quantum measurement theory and classical filter theory into a time-evolving hybrid quantum and classical trajectory. The forward-backward analysis that permits smoothed estimates of classical hidden Markov models has a counterpart in the theory of retrodiction and past quantum states. As a specific example, we apply our hybrid trajectory and past-quantum-state theory to the sensing of a fluctuating magnetic field by microwave interrogation of a single quantum spin.

中文翻译：

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时间相关扰动的量子估计

我们分析了作用于连续监测量子系统的瞬态扰动的估计。我们通过隐马尔可夫模型描述扰动的时间波动，并将量子测量理论和经典滤波器理论结合成时间演化的混合量子和经典轨迹。允许对经典隐马尔可夫模型进行平滑估计的前向-后向分析在追溯理论和过去的量子态中有对应物。作为一个具体的例子，我们将我们的混合轨迹和过去量子态理论应用于通过单个量子自旋的微波询问来感测波动的磁场。