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

A quantum process is called non-Markovian when memory effects take place during its evolution. Quantum non-Markovianity is a phenomenon typically associated with the information back-flow from the environment to the principal system, however it has been shown that such an effect is not necessary. In particular, maximum quantum non-Markovianity can be achieved without any physical transmission of information. In this work, it is shown that time-homogeneity is a sufficient condition for a non-Markovian quantum process to originate from an information back-flow effect. As a characteristic example, the protocol of measurement-free teleportation is suggested as a time-homogeneous maximally non-Markovian quantum process, in both discrete and continuous-variable systems. Finally, given the resource-like role of entanglement in teleportation protocol, the relationship between this property and non-Markovianity is elucidated.