System-environment quantum information flow

The characterization of the dynamics of a quantum system that interacts with an environment reveals how quantum resources are transformed or consumed during the action of a physical process. In some scenarios, such consumption is reversed due to an environment-induced back-action that causes the return of the information to the system. This phenomenon can be related to existence of non-Markovian mechanisms in the environment and such 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 work, we show how a quantum resource, named quantum coherence, propagates from the main system to an environment, using as 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, as well as its return from the environment to the main system. Finally, we connect the conditions for the emergence of this dynamics to the existence of quantum Darwinism.