Adaptive quantum state estimation for dynamic quantum states

Accurate estimation of unknown quantum states using limited number of samples is very important but difficult task using fixed measurement basis states since the best local unbiased estimator (LUE) for estimating the parameter depends, in general, on the unknown parameter itself. In order to solve this problem, Nagaoka advocated an adaptive quantum state estimation (AQSE) procedure [1], where the measurement basis states are adaptively selected for each measurement result. Fujiwara proved the strong consistency and asymptotic efficiency for AQSE [2]. Recently, AQSE has been demonstrated by us for the linear polarizations of photons [3]. However, AQSE was designed for a static quantum state, and was not applicable to dynamic states where quantum states change in time. Here, we propose a new protocol, sequential adaptive quantum state estimation (SAQSE) for dynamic quantum states. Our numerical simulation (shown below) clearly show that the estimated value given by SAQSE can follow the true value changing in time whereas AQSE fails. We believe this new protocol will open up the use of quantum state estimation for various applications including biology, e.g. monitoring the motion of fluorescent molecules.