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A quantum process is called non-Markovian when memory effects take placeduring its evolution. Quantum non-Markovianity is a phenomenon typicallyassociated with the information back-flow from the environment to the principalsystem, however it has been shown that such an effect is not necessary. In thiswork, we establish a connection between quantum non-Markovianity and theprotocol of quantum teleportation in both discrete and continuous-variablesystems. We also show how information flows during a teleportation protocolbetween the principal system and the environment in a bidirectional way leadingup to a state revival. Finally, given the resource-like role of entanglement inthe teleportation protocol, the relationship between this property andnon-Markovianity is also elucidated.

Information back-flow in quantum non-Markovian dynamics and its connection to teleportation