  Detuned systems can spontaneously achieve a synchronous dynamics and display
robust quantum correlations in different local and global dissipation regimes.
Beyond the Markovian limit, information backflow from the environment becomes a
crucial mechanism whose interplay with spontaneous synchronization is unknown.
Considering a model of two coupled qubits, one of which interacts with a
dissipative environment, we show that non-Markovianity is highly detrimental
for the emergence of synchronization, for the latter can be delayed and
hindered because of the presence of information backflow. The results are
obtained considering both a master equation approach and a collision model
based on repeated interactions, which represents a very versatile tool to
tailor the desired kind of environment.
