System-environment quantum information flow

The return of the information from the environment to the system is a phenomenon that can be related to the existence of non-Markovian mechanisms in the environment, and such a transformation of resources can be useful for quantum information applications. Thus, understanding the details of the system-environment information dynamics, i.e., the transference of quantum resources, is of key importance to design noise-resilient quantum technologies. In this Letter, we show how a quantum resource propagates from the main system to an environment, using as a model a single qubit coupled to two linear chains of qubits, and also the information dynamics among the environment qubits. In this way, we characterize the propagation of information leaving the main qubit and going through the environment. Finally, we connect the conditions for the emergence of this dynamics to the existence of quantum Darwinism.