Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics
Operator Algebras
2019-11-04 v4 Probability
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1804.03510,
title = {Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics},
author = {Akio Fujiwara and Koichi Yamagata},
journal= {arXiv preprint arXiv:1804.03510},
year = {2019}
}
Comments
Introduction is enriched and some proofs are deferred to the appendix. arXiv admin note: text overlap with arXiv:1703.07535