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Entropic characterization of coherence in quantum evolutions

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.