We address a general problem to detect a possible correlation in quantum mechanical systems from the information of sub-systems. As a natural but a powerful property, if the sub-system is in a pure state, then we can conclude no correlations with any other environment. On the other hand, if the partial system is in a mixed state, any static property cannot be used to determine a possible correlation. In this talk, we propose to use dynamical information and prove a certain statement which can be used for this purpose. A quantitative estimation of correlations is also shown for bounded Hamiltonians, which generalize the statement. This also clarify the role of correlations in the mechanism of a decoherence. For unbounded Hamiltonians, there appears a sort of domain-problem, and some modifications are necessary.