The quantum Markovianity criterion based on correlations under random unitary qudit dynamical evolutions.

Random unitary dynamical evolutions play an important role in characterizing quantum Markovianity. By exploiting the maximally entangled state under the representation of a set of generalized unitary Weyl operators, we present a necessary and sufficient condition for quantum Markovianity in d-level systems from the perspective of quantum mutual information. Moreover, we analyze three quantum Markovianity criteria among divisibility, BLP and LFS 0 to establish their connections and differences. It is shown that they coincide in many special cases, but different in general, and Markovianity in the sense of LFS 0 is less restrictive than Markovianities in the sense of divisibility and BLP by detailed examples. [ABSTRACT FROM AUTHOR]