Noncommutative Lebesgue decomposition with application to quantum local asymptotic normality

TL;DR

This paper introduces a noncommutative Lebesgue decomposition framework to extend quantum local asymptotic normality to a broader class of quantum statistical models, including mixed-rank density operators.

Contribution

It develops a novel noncommutative Lebesgue decomposition approach to generalize quantum local asymptotic normality for mixed-rank quantum models.

Findings

Extended quantum local asymptotic normality to mixed-rank models

Provided a noncommutative Lebesgue decomposition framework

Generalized previous quantum statistical results

Abstract

We develop a theory of local asymptotic normality in the quantum domain based on a noncommutative extension of the Lebesgue decomposition. This formulation gives a substantial generalization of the previous paper [Yamagata, Fujiwara, and Gill (2013). Ann. Statist., 41, 2197-2217.], extending the scope of the quantum local asymptotic normality to a wider class of quantum statistical models that comprise density operators of mixed ranks.