We develop a theory of local asymptotic normality in the quantum domain based on a novel quantum analogue of the log-likelihood ratio. This formulation is applicable to any quantum statistical model satisfying a mild smoothness condition. As an application, we prove the asymptotic achievability of the Holevo bound for the local shift parameter.
"Quantum local asymptotic normality based on a new quantum likelihood ratio." Ann. Statist. 41 (4) 2197 - 2217, August 2013. https://doi.org/10.1214/13-AOS1147