  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.
