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Quantum Darwinism explains the emergence of a classical description ofobjects in terms of the creation of many redundant registers in an environmentcontaining their classical information. This amplification phenomenon, whereonly classical information reaches the macroscopic observer and through whichdifferent observers can agree on the objective existence of such object, hasbeen revived lately for several types of situations, successfully explainingclassicality. We explore quantum Darwinism in the setting of an environmentmade of two level systems which are initially prepared in the ground state ofthe XX model, which exhibits different phases; we find that the differentphases have different ability to redundantly acquire classical informationabout the system, being the "ferromagnetic phase" the only one able to completequantum Darwinism. At the same time we relate this ability to how non-Markovianthe system dynamics is, based on the interpretation that non-Markovian dynamicsis associated to back flow of information from environment to system, thusspoiling the information transfer needed for Darwinism. Finally, we exploremixing of bath registers by allowing a small interaction among them, findingthat this spoils the stored information as previously found in the literature.

Quantum Darwinism and non-Markovian dissipative dynamics from quantum phases of the spin-1/2 XX model