The Annals of Statistics
- Ann. Statist.
- Volume 41, Number 4 (2013), 2197-2217.
Quantum local asymptotic normality based on a new quantum likelihood ratio
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.
Ann. Statist., Volume 41, Number 4 (2013), 2197-2217.
First available in Project Euclid: 23 October 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 81P50: Quantum state estimation, approximate cloning
Secondary: 62F12: Asymptotic properties of estimators
Yamagata, Koichi; Fujiwara, Akio; Gill, Richard D. Quantum local asymptotic normality based on a new quantum likelihood ratio. Ann. Statist. 41 (2013), no. 4, 2197--2217. doi:10.1214/13-AOS1147. https://projecteuclid.org/euclid.aos/1382547518
- Supplementary material: Supplementary material to “Quantum local asymptotic normality based on a new quantum likelihood ratio”. Section A is devoted to proofs of Lemma 2.6, Theorems 2.9 and 2.10, Corollary 2.11, and Theorem 3.1. Section B is devoted to a brief account of quantum estimation theory, including quantum logarithmic derivatives, the commutation operator, the Holevo bound, estimation theory for quantum Gaussian shift models and for pure state models.