  By using relative entropy of coherence, we characterize the coherence gain
induced by some quantum evolutions, including the cohering power of unitary
operations and the decohering power of quantum operations. We find that the
cohering power of the controlled unitary operation can be reduced to the
cohering power of the corresponding unitary operation. We observe that the
global coherence generated via incoherent operation applied to the system and
an incoherent ancilla do not exceed the amount of coherence contained in the
initial system. Our result provides a much tighter lower bound of coherence for
the initial quantum state, and give an interesting chain of inequalities for
coherence, quantum correlation and entanglement. We also strengthen the
relations between quantum correlations and coherence.
