  The developing of (non-Markovian) memory effects strongly depends on the
underlying system-environment dynamics. Here we study this problem in
multipartite arrangements where all subsystems are coupled to each other by
non-diagonal Markovian (Lindblad) dephasing mechanisms. Taking as system and
environment arbitrary sets of complementary subsystems it is shown that both
operational and non-operational approaches to quantum non-Markovianity can be
characterized in an exact analytical way. Similarly to previous studies about
dissipative-entanglement-generation in this kind of dynamics [Seif, Wang, and
Clerk, Phys. Rev. Lett. 128, 070402 (2022)], we found that memory effects can
only emerge when a time-reversal symmetry is broken. Nevertheless, it is also
found that departures from Markovianity can equivalently be represented through
a statistical mixture of Markovian dephasing dynamics, which does not involve
any system-environment entanglement. Specific bipartite and multipartite
dynamics exemplify the main general results.

Quantum Physics