EFFICIENCY OF ESTIMATORS FOR LOCALLY ASYMPTOTICALLY NORMAL QUANTUM STATISTICAL MODELS

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.

Automated summary

We establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models, allowing us to study the asymptotic efficiency of quantum estimators and providing a tight lower bound beyond the i.i.d. assumption. This complements the theory of quantum contiguity and establishes a solid foundation of weak quantum local asymptotic normality.