  We study the effects of quantum fluctuations on the transport properties of
multiband superconductors near a pair-breaking quantum critical point. For this
purpose, we consider a minimal model of the quantum phase transition in a
system with two nested two-dimensional Fermi surfaces. Under the assumption
that doping the system adds nonmagnetic impurities but does not change the
densities of carriers, we include disorder potentials that render both intra-
and interband collisions. Interband scattering leads to full suppression of the
unconventional $s^{\pm}$ superconducting order similar to the effect of
paramagnetic impurities in isotropic single-band superconductors. We use the
diagrammatic technique of quantum field theory to compute the corrections to
electrical conductivity in a normal state due to superconducting fluctuations
in the entire low-temperature quantum regime. We show that the sign of the
conductivity correction depends on how the quantum critical point is approached
in the phase diagram. We contrast our findings to existing approaches to this
problem based on the renormalization group, time-dependent Ginzburg-Landau
phenomenology, and effective bosonic action field theories.
