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.
"Noncommutative Lebesgue decomposition and contiguity with applications in quantum statistics." Bernoulli 26 (3) 2105 - 2142, August 2020. https://doi.org/10.3150/19-BEJ1185