Efficiency of estimators for locally asymptotically normal quantum statistical models
本文为局部渐近正态量子统计模型建立了渐近表示定理，用于研究量子估计量的渐近效率，并给出了超越独立同分布假设的通用紧下界。
We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators, such as quantum regular estimators and quantum minimax estimators, leading to a universal tight lower bound beyond the i.i.d. assumption. This formulation complements the theory of quantum contiguity developed in the previous paper [Fujiwara and Yamagata, Bernoulli 26 (2020) 2105–2141], providing a solid foundation of the theory of weak quantum local asymptotic normality.