  We consider the so-called measure once finite quantum automata model
introduced by Moore and Crutchfield in 2000. We show that given a language
recognized by such a device and a linear context-free language, it is
recursively decidable whether or not they have a nonempty intersection. This
extends a result of Blondel et al. which can be interpreted as solving the
problem with the free monoid in place of the family of linear context-free
languages.
