  We show that quantum vortex-loop proliferation may be one possible
explanation of the super-long-range proximity effect observed in an insulating
underdoped cuprate, using the dual theory of quantum vortices. As a test of
this scenario, we propose that a dual proximity effect experiment can confirm
the superfluid motion of the quantum vortices in the vortex-proliferated
insulator and can measure the divergent correlation lengths near the
superconductor-insulator transition.
