Abstract
We critically examine the role that correlations established between a system and fragments of its environment play in characterising the ensuing dynamics. We employ a dephasing model with different initial conditions, where the state of the initial environment represents a tunable degree of freedom that qualitatively and quantitatively affects the correlation profiles, but nevertheless results in the same reduced dynamics for the system. We apply recently developed tools for the characterisation of non-Markovianity to carefully assess the role that correlations, as quantified by the (quantum) Jensen–Shannon divergence and relative entropy, as well as changes in the environmental state, play in whether the conditions for classical objectivity within the quantum Darwinism paradigm are met. We demonstrate that for precisely the same non-Markovian reduced dynamics of the system arising from different microscopic models, some exhibit quantum Darwinistic features, while others show that no meaningful notion of classical objectivity is present. Furthermore, our results highlight that the non-Markovian nature of an environment does not a priori prevent a system from redundantly proliferating relevant information, but rather it is the system’s ability to establish the requisite correlations that is the crucial factor in the manifestation of classical objectivity.
Highlights
IntroductionThe necessity for effective means to describe how a quantum system interacts with its surrounding environment has precipitated a burgeoning area of research
Reverting to a full microscopic description, where the system and environment interact and evolve according to an overall unitary dynamics, reveals that the correlations established between the system and the environment during their interaction play an important role in the resulting open dynamics of the system [1,2]
These correlations are the basis for notions of classical objectivity [3–7] and are known to play a key role in the characterisation of the dynamics, in particular, if the system undergoes a Markovian or non-Markovian evolution [8,9]
Summary
The necessity for effective means to describe how a quantum system interacts with its surrounding environment has precipitated a burgeoning area of research. A given open system dynamics does not arise from a unique microscopic system–environment model, and rather, there are infinitely many system–environment models that result in the same system evolution [21] Such an insight calls for a more careful analysis of the information exchanges between the system and its environment, allowing to more precisely pin down the relevant contributions which give rise to, for example, Markovian vs non-Markovian dynamics [22], or establish the conditions for classical objectivity [23–25]. This becomes subtle since under such a microscopic picture, the environment is typically composed of many constituent subsystems, and it is relevant to assess the complementary role that global correlations established between the system and the whole environment play compared to correlations shared between the system and smaller environmental fragments.
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