  Many quantum mechanical experiments can be viewed as multi-round interactive
protocols between known quantum circuits and an unknown quantum process. Fully
quantum "coherent" access to the unknown process is known to provide an
advantage in many discrimination tasks compared to when only incoherent access
is permitted, but it is unclear if this advantage persists when the process is
noisy. Here, we show that a quantum advantage can be maintained when
distinguishing between two noisy single qubit rotation channels. Numerical and
analytical calculations reveal a distinct transition between optimal
performance by fully coherent and fully incoherent protocols as a function of
noise strength. Moreover, the size of the region of coherent quantum advantage
shrinks inverse polynomially in the number of channel uses, and in an
intermediate regime an improved strategy is a hybrid of fully-coherent and
fully-incoherent subroutines. The fully coherent protocol is based on quantum
signal processing, suggesting a generalizable algorithmic framework for the
study of quantum advantage in the presence of realistic noise.
