Efficiency of estimators for locally asymptotically normal quantum statistical models

TL;DR

This paper develops an asymptotic representation theorem for quantum statistical models, enabling analysis of estimator efficiency and establishing a universal lower bound beyond i.i.d. assumptions.

Contribution

It introduces a new asymptotic representation theorem for quantum models, extending the theory of quantum local asymptotic normality and efficiency bounds.

Findings

Established an asymptotic representation theorem for quantum models

Derived a universal tight lower bound for quantum estimators

Extended the theory of quantum contiguity and local asymptotic normality

Abstract

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.