Quantum non-Markovianity and information back-flow in quantum teleportation

Quantum non-Markovianity (QNM) is a phenomenon associated to the information back-flow from the environment to the dynamical system, i.e., dynamical systems evolving through quantum channels with memory effects. In this work, we establish a connection between QNM and the protocol of quantum teleportation (QT). In particular, we consider the quantum computation-based QT of discrete-variable states [Brassard et al., Phys. D 120, 43 (1998)] and the all-optical QT of continuous-variable states [Ralph, Opt. Lett. 24, 348 (1999)] to show how information from the input state (system) moves to the environment and subsequently returns back to create the output state (which is ideally identical to the input state). Given that in QT protocols entanglement is utilized as a resource, a connection between entanglement and QNM is also drawn. Finally, the interesting role that QNM plays in quantum information protocols is discussed, given that QT protocols form the basis of various tasks in quantum communication and computation.