Detecting Non-Markovianity via Quantified Coherence: Theory and Experiments

The dynamics of open quantum systems and manipulation of quantum resources are both of fundamental interest in quantum physics. Here, we investigate the relation between quantum Markovianity and coherence, providing an effective way for detecting non-Markovianity based on the \textit{quantum-incoherent relative entropy of coherence} ($\mathcal{QI}$ REC). We theoretically show the relation between completely positive (CP) divisibility and the monotonic behavior of the $\mathcal{QI}$ REC. Also we implement an all-optical experiment to demonstrate that the behavior of the $\mathcal{QI}$ REC is coincident with the entanglement shared between the system and the ancilla for both Markovian and non-Markovian evolution; while other coherence-based non-Markovian information carriers violate monotonicity, even in Markovian processes. Moreover, we experimentally observe that non-Markovianity enhances the ability of creating coherence on an ancilla. This is the first experimental study of the relation between dynamical behavior of the $\mathcal{QI}$ REC and the phenomenon of information backflow. Moreover, our method for detecting non-Markovianity is applicable to general quantum evolutions.