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.
Funding Statement
The present study was supported by JSPS KAKENHI Grant Numbers JP17H02861, JP22K03466, and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number JPMXS0120351339.
Citation
Akio Fujiwara. Koichi Yamagata. "Efficiency of estimators for locally asymptotically normal quantum statistical models." Ann. Statist. 51 (3) 1159 - 1182, June 2023. https://doi.org/10.1214/23-AOS2285
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