  A possibility to detect correlations between two quantum mechanical systems
only from the information of a subsystem is investigated. For generic cases, we
prove that there exist correlations between two quantum systems if the
time-derivative of the reduced purity is not zero. Therefore, an
experimentalist can conclude non-zero correlations between his/her system and
some environment if he/she finds the time-derivative of the reduced purity is
not zero. A quantitative estimation of a time-derivative of the reduced purity
with respect to correlations is also given. This clarifies the role of
correlations in the mechanism of decoherence in open quantum systems.
