  Amplitude amplification is one of primary tools in building algorithms for
quantum computers. This technique generalizes key ideas of the Grover search
algorithm. Potentially useful modifications are connected with changing phases
in the rotation operations and replacing the intermediate Hadamard transform
with arbitrary unitary one. In addition, arbitrary initial distribution of the
amplitudes may be prepared. We examine trade-off relations between measures of
quantum coherence and the success probability in amplitude amplification
processes. As measures of coherence, the geometric coherence and the relative
entropy of coherence are considered. In terms of the relative entropy of
coherence, complementarity relations with the success probability seem to be
the most expository. The general relations presented are illustrated within
several model scenarios of amplitude amplification processes.
