Minimax nonparametric estimation of pure quantum states
该研究将经典统计中的Pinsker定理推广到量子领域，建立了量子高斯白噪声模型中位移向量的渐近最小最大估计，并进一步得到纯量子态估计的最优性结果，适用于所有可能的测量和迹范数距离。
In classical statistics, Pinsker’s theorem provides an exact asymptotic minimax bound in nonparametric estimation, improving upon optimal rates of convergence results. We obtain a quantum version of the theorem by establishing asymptotic minimax results for estimation of the displacement vector in a quantum Gaussian white noise model, given by a sequence of shifted vacuum states. Analogous results are then obtained for estimation of a general pure state from an ensemble of identically prepared, independent quantum systems, using the recently established local asymptotic equivalence to the quantum Gaussian white noise model. Optimality holds with respect to the most fundamental distance measure for quantum states, that is, trace norm distance, and in a true quantum sense, allowing for all possible measurements. Adaptive estimators are also obtained for the above cases. As an application, we obtain asymptotic minimax adaptive estimators for Wigner functions of pure states.