Open Access
August 2020 Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics
Akio Fujiwara, Koichi Yamagata
Bernoulli 26(3): 2105-2142 (August 2020). DOI: 10.3150/19-BEJ1185


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, Ann. Statist. 41 (2013) 2197–2217], yielding substantial enlargement of the scope of quantum statistics.


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Akio Fujiwara. Koichi Yamagata. "Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics." Bernoulli 26 (3) 2105 - 2142, August 2020.


Received: 1 August 2019; Revised: 1 December 2019; Published: August 2020
First available in Project Euclid: 27 April 2020

zbMATH: 07193954
MathSciNet: MR4091103
Digital Object Identifier: 10.3150/19-BEJ1185

Keywords: contiguity , Lebesgue decomposition , likelihood ratio , local asymptotic normality , quantum statistics

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 3 • August 2020
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