  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.
