Quantum local asymptotic normality based on a new quantum likelihood ratio

Koichi Yamagata, Akio Fujiwara, Richard D. Gill

The Annals of Statistics · 2013 · Volume 41 · Issue 4

Abstract

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.

Keywords

62F12, 81P50, Holevo bound, Quantum local asymptotic normality, quantum log-likelihood ratio

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