  In this paper, we study measures of quantum non-Markovianity based on the
conditional mutual information. We obtain such measures by considering multiple
parts of the total environment such that the conditional mutual information can
be defined in this multipartite setup. The benefit of this approach is that the
conditional mutual information is closely related to recovery maps and Markov
chains; we also point out its relations with the change of distinguishability.
We study along the way the properties of leaked information which is the
conditional mutual information that can be back flowed, and we use this leaked
information to show that the correlated environment is necessary for nonlocal
memory effect.
