Robust quantum Kalman filtering under the phase uncertainty of the probe-laser

The quantum Kalman filter has enough specification for accurate estimation and control in linear quantum systems, though this holds only in the case when the system parameters are completely known as in the classical case. In this paper, we consider an optical system containing an uncertain parameter in the probe-laser and propose a robust filtering scheme against this uncertainty. The filter estimates the uncertain parameter using an additional hardware probe sensor and adaptively changes the filtering algorithm so that it acquires the better estimation performance near to that of the optimal true filter. The robustness is explicitly evaluated in terms of the estimation error and is also numerically demonstrated.