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August 2013 Quantum local asymptotic normality based on a new quantum likelihood ratio
Koichi Yamagata, Akio Fujiwara, Richard D. Gill
Ann. Statist. 41(4): 2197-2217 (August 2013). DOI: 10.1214/13-AOS1147

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.

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Koichi Yamagata. Akio Fujiwara. Richard D. Gill. "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

Information

Published: August 2013
First available in Project Euclid: 23 October 2013

zbMATH: 1278.81050
MathSciNet: MR3127863
Digital Object Identifier: 10.1214/13-AOS1147

Subjects:
Primary: 81P50
Secondary: 62F12

Keywords: Holevo bound , Quantum local asymptotic normality , quantum log-likelihood ratio

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • August 2013
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