  Quantum Darwinism extends the traditional formalism of decoherence to explain
the emergence of classicality in a quantum universe. A classical description
emerges when the environment tends to redundantly acquire information about the
pointer states of an open system. In light of recent interest, we apply the
theoretical tools of the framework to a qubit coupled with many bosonic
sub-environments. We examine the degree to which the same classical information
is encoded across collections of: (i) complete sub-environments, and (ii)
residual "pseudomode" components of each sub-environment, the conception of
which provides a dynamic representation of the reservoir memory. Overall,
significant redundancy of information is found as a typical result of the
decoherence process. However, by examining its decomposition in terms of
classical and quantum correlations, we discover classical information to be
non-redundant in both cases (i) and (ii). Moreover, with the full collection of
pseudomodes, certain dynamical regimes realize opposite effects, where either
the total classical or quantum correlations predominantly decay over time.
Finally, when the dynamics are non-Markovian, we find that redundant
information is suppressed in line with information back-flow to the qubit. By
quantifying redundancy, we concretely show it to act as a witness to
non-Markovianity in the same way as the trace distance does for nondivisible
dynamical maps.
