Non-Markovianity has recently attracted large interest due to significant
advances in its characterization and its exploitation for quantum information
processing. However, up to now, only non-Markovian regimes featuring
environment to system backflow of information (strong non-Markovianity) have
been experimentally simulated. In this work, using an all-optical setup we
simulate and observe the so-called weak non-Markovian dynamics. Through full
process tomography, we experimentally demonstrate that the dynamics of a qubit
can be non-Markovian despite an always increasing correlation between the
system and its environment which, in our case, denotes no information backflow.
We also show the transition from the weak to the strong regime by changing a
single parameter in the environmental state, leading us to a better
understanding of the fundamental features of non-Markovianity.Comment: v2: final versio