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.

翻译：本文建立了局部渐近正态量子统计模型的渐近表示定理。该定理使我们能够研究量子估计量（如量子正则估计量和量子极小极大估计量）的渐近效率，从而在独立同分布假设之外导出一个普适的紧下界。这一理论框架完善了先前论文[Fujiwara and Yamagata, Bernoulli 26 (2020) 2105-2141]中发展的量子邻接理论，为弱量子局部渐近正态性理论奠定了坚实基础。