The coherent superposition of quantum states is one of the characteristic features of quantum mechanics, and it is also physical resource of quantum information processing. The coherence of quantum system can not last a long time as the effect of the noise. How well has the noisy channel preserved the quantum coherence of the quantum system? Based on the relative entropy of coherence, in this paper, we discuss the coherence, entanglement and quantum correlations in the bipartite quantum system. To discuss the effect of the noise, we then give a definition of the decayed amount of the maximal quantum coherence, i.e., the decay of coherence. Then we obtain that the uncertainty relations between entanglement and the coherence with respect to the noisy models. Finally, we used the measure of the decay of coherence to discuss how well several noisy channels preserves the coherence.
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