Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics

Abstract

We herein develop a theory of contiguity in the quantum domain based upon a novel quantum analogue of the Lebesgue decomposition. The theory thus formulated is pertinent to the weak quantum local asymptotic normality introduced in the previous paper [Yamagata, Fujiwara, and Gill, \textit{Ann. Statist.}, \textbf{41} (2013) 2197-2217.], yielding substantial enlargement of the scope of quantum statistics.

arXiv commentIntroduction is enriched and some proofs are deferred to the appendix. arXiv admin note: text overlap with arXiv:1703.07535

References in corpus (6)

• State estimation for large ensembles
• Local asymptotic normality for finite dimensional quantum systems
• Quantum local asymptotic normality based on a new quantum likelihood ratio
• Attaining the ultimate precision limit in quantum state estimation
• Local asymptotic normality for qubit states
• Local asymptotic normality in quantum statistics