Quantum Darwinism attempts to explain the emergence of objective reality of the state of a quantum system in terms of redundant information about the system acquired by independent non interacting fragments of the environment. The consideration of interacting environmental elements gives rise to a rich phenomenology, including the occurrence of non-Markovian features, whose effects on objectification a' la quantum Darwinism needs to be fully understood. We study a model of local interaction between a simple quantum system and a multi-mode environment that allows for a clear investigation of the interplay between information trapping and propagation in the environment and the emergence of quantum Darwinism. We provide strong evidence of the correlation between non-Markovianity and quantum Darwinism in such a model, thus providing strong evidence of a potential link between such fundamental phenomena.The quantum Darwinism paradigm is one of the most recent and convincing attempt to explain the emergence of objective reality out of superpositions of quantum states (for a review see [1]). In this framework, the first key mechanism responsible of the transition from quantum to classical is the coupling of the system with an environment which acquires information about the state of the system with respect the so called pointer states, namely the eigenstates of the observable which is coupled with the environment [2-4]. If the system is in a specific pointer state it is left undisturbed by such coupling, if however the system is in a coherent superposition of pointer states it gets entangled with the environment. An external observer who can access the environment can therefore acquire informations on the state of the system, leading to its objective existence.The second key ingredient at the basis of quantum Darwinism is the particular structure of the environmental states which get entangled with the pointer state. The basic idea is that in a real scenario the environment degrees of freedom are not traced out but rather accessed by different observers. The assumption is that information on the state of the system is redundantly encoded in multiple, independent fragments of the environment, which we assume to consist of a large set of non interacting units. External observers can read the information on the system contained in separate, locally accessible fragments of the environment, with each fragment containing the same information on the system, this leading to objective reality of the system state [5][6][7]. This is what naturally happens when an initial coherent superposition of system pointer states |Ψ S = n k=1 ψ k |π k S evolves into a joint system-environment state with a branching structurewhere the information about the system state |π k S is imprinted into multiple copies of environmental states |η k , thus becoming accessible to individual, distinct observers, that access separate fragments of the environment. The phenomenology of quantum Darwinism has attracted a robust body of work, recently [8-18, 23, ...
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