Title: Robust Guaranteed-Cost Adaptive Quantum Phase Estimation,
Abstract: Quantum parameter estimation plays a key role in many fields like quantum
computation, communication and metrology. Optimal estimation allows one to
achieve the most precise parameter estimates, but requires accurate knowledge
of the model. Any inevitable uncertainty in the model parameters may heavily
degrade the quality of the estimate. It is therefore desired to make the
estimation process robust to such uncertainties. Robust estimation was
previously studied for a varying phase, where the goal was to estimate the
phase at some time in the past, using the measurement results from both before
and after that time within a fixed time interval up to current time. Here, we
consider a robust guaranteed-cost filter yielding robust estimates of a varying
phase in real time, where the current phase is estimated using only past
measurements. Our filter minimizes the largest (worst-case) variance in the
allowable range of the uncertain model parameter(s) and this determines its
guaranteed cost. It outperforms in the worst case the optimal Kalman filter
designed for the model with no uncertainty, that corresponds to the center of
the possible range of the uncertain parameter(s). Moreover, unlike the Kalman
filter, our filter in the worst case always performs better than the best
achievable variance for heterodyne measurements, that we consider as the
tolerable threshold for our system. Furthermore, we consider effective quantum
efficiency and effective noise power, and show that our filter provides the
best results by these measures in the worst case.