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The total correlations in a bipartite quantum system are measured by the quantum mutual information $\mathcal{I}$, which consists of quantum discord and classical correlation. However, recent results in quantum information shows that coherence, which is a part of total correlation, is more general and more fundamental than discord. The role of coherence in quantum resource theories is worthwhile to investigate. We first study the relation between quantum discord and coherence by reducing the difference between them. And then, we consider the dynamics of quantum discord, classical correlations and quantum coherence under incoherent quantum channels. We discover that coherence indicate the behavior of quantum discord (classical correlation) for times $t\bar t$. What is more, the coherence frozen and decay indicate the quantum discord and classical correlation frozen and decay respectively., Comment: 7pages, 5figures

We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ($\mathcal{C}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure ($\mathcal{C}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of database, no matter using $\mathcal{C}_r$ or $\mathcal{C}_{l_1}$. In generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichny's inequality are not violated., 9 pages, 5 figures

We introduce the concept of monogamy deficit for quantum correlation by combining together two types of monogamy inequalities depending on different measurement sides. For tripartite pure state, we demonstrate a relation which connects two types of monogamy inequalities for quantum discord and provide the difference between them. By using this relation, we obtain an unified physical interpretation for these two monogamy deficit. In addition, we find an interesting fact that there is a general monogamy condition for several quantum correlations for tripartite pure states. We then provide a necessary and sufficient condition for the establishment of one kind of monogamy inequality for tripartite mixed state and generalize it to multipartite quantum state., 8 pages, 1 figure