  We study the evolution of a general open quantum system when the system and
its environment are initially correlated. We show that the trace distance
between two states of the open system can increase above its initial value, and
derive tight upper bounds for the growth of the distinguishability of open
system states. This represents a generalization of the contraction property of
quantum dynamical maps. The obtained inequalities can be interpreted in terms
of the exchange of information between the system and the environment, and lead
to a witness for system-environment correlations which can be determined
through measurements on the open system alone.
