The formalism of quantum estimation theory, focusing on the quantum and classical Fisher information, is applied to the estimation of the coupling strength in an optomechanical system. In order to estimate the optomechanical coupling, we have considered a cavity optomechanical model with non-Markovian Brownian motion of the mirror and employed input-output formalism to obtain the cavity output field. Our estimation scenario is based on balanced homodyne photodetection of the cavity output field. We have explored the difference between the associated measurement-dependent classical Fisher information and the quantum Fisher information, thus addressing the question of whether it is possible to reach the lower bound of the mean-squared error of an unbiased estimator by means of balanced homodyne detection. We have found that the phase of the local oscillator in the homodyne detection is crucial; certain quadrature measurements allow very accurate estimation.

中文翻译：

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基于Fisher信息的光机械耦合强度估计

量子估计理论的形式主义，着重于量子和经典Fisher信息，被应用于光机械系统中耦合强度的估计。为了估计光机耦合，我们考虑了具有非马尔可夫布朗运动镜的腔光机模型，并采用输入输出形式来获得腔输出场。我们的估计方案基于腔体输出场的平衡零差光电检测。我们已经研究了相关的依赖于测量的经典Fisher信息和量子Fisher信息之间的区别，从而解决了是否有可能通过平衡零差检测来达到无偏估计量均方误差的下限的问题。 。我们发现零差检测中本地振荡器的相位至关重要。某些正交测量可以进行非常精确的估计。