  In this article, we study the dynamics of quantum correlation measures such
as entanglement and measurement-induced nonlocality (MIN). Starting from an
arbitrary Bell diagonal mixed states under Markovian local noise such as
bit-phase flip, depolarizing and generalized amplitude damping channel, we
provide the decays of the entanglement measured by concurrence and quantum
correlation captured by different forms of MIN (trace distance, Hilbert-Schmidt
norm and relative entropy) as a function of the decoherence parameters. The
effect of local noises on the dynamical behaviors of quantum correlation is
observed. We show the existence of specific and important features of MIN such
as revival, noise robustness and sudden change with respect to decoherence
parameter. It is observed that all the noises cause sudden death of
entanglement for partially entangled states. Further, we show the existence of
separable quantum states with non-zero quantum correlations in terms of MIN.
