  Coherent errors in a quantum system can, in principle, build up much more
rapidly than incoherent errors, accumulating as the square of the number of
qubits in the system rather than linearly. I show that only channels dominated
by a unitary rotation can display such behavior. A maximally sensitive set of
states is a set such that if a channel is capable of quadratic error scaling,
then it is present for at least one sequence of states in the set. I show that
the GHZ states in the X, Y, and Z bases form a maximally sensitive set of
states, allowing a straightforward test to identify coherent errors in a
system. This allows us to identify coherent errors in gates and measurements to
within a constant fraction of the maximum possible sensitivity to such errors.
A related protocol with simpler circuits but less sensitivity can also be used
to test for coherent errors in state preparation or if the noise in a
particular circuit is accumulating coherently or not.
