Quantum Darwinism and non-Markovianity in a model of quantum harmonic oscillators

Abstract

To explain aspects of the quantum-to-classical transition, quantum Darwinism explores the fact that, due to interactions between a quantum open system and its surrounding environment, information about the system can be spread redundantly to the environment. Here we recall that there are in the literature two distinct and non-equivalent ways to make this statement precise and quantitative. We first point out the difference with some simple but illustrative examples. We then consider a model where Darwinism can be seen from both perspectives. Moreover, the non-Markovianity of our model can be varied with a parameter. In a recent work [F. Galve et al., Sci. Reps. 6, 19607 (2016)], the authors concluded that quantum Darwinism can be hindered by non-Markovianity. We depart from their analysis and argue that, from both perspectives to quantum Darwinism, there is no clear relationship between non-Markovianity and quantum Darwinism in our model. FIG. 1: Three qualitatively distinct possibilities for a partial information plot (PIP). The solid line (a) corresponds to a case where a small fraction of the environment already has average mutual information close to H(S), being the signature of quantum Darwinism. The linear profile (b) can be seen (approximately) in our model for small interaction times (see Sec. V). In profile (c), f δ is close to 0.5, so the redundancy is very small. This kind of profile can be obtained from random pure states drawn according to the Haar measure [13].

Suppressing information storage in a structured thermal bath: Objectivity and non-Markovianity

“…[15], based on the importance of the possibility of information extraction, i.e., measurable, distinguishable and accessible information, that is not necessarily taken into account in the quantum Darwinism paradigm. A. Quantum Darwinism Quantum Darwinism's approach was used to treat a wide range of systems, like spin [28][29][30][31][32], and photonic [33][34][35][36] environments, harmonic oscillator [37] and Brownian [38,39] models, and experimentally in quantum dots [40], and photonic [33,35] setups. To study quantum Darwinism, we focus on correlations between fragments of the environment and the system.…”

Roads to objectivity: Quantum Darwinism, Spectrum Broadcast Structures, and Strong quantum Darwinism – a review

“…in [14][15][16]. Quantum Darwinism literature is quite numerous and this is just a small sample (for the most recent research see e. g. [17]). Recently there appeared also experiments aimed at observing (3) [18][19][20], which I discuss separately in Section VIII.…”

Quantum Darwinism in a Composite System: Objectivity versus Classicality

“…Recent studies have shown that the emergence of a redundancy plateau in the mutual information, the characteristic signal of quantum Darwinism, may not imply classical objectivity [4,8,12]. Several critical analyses of quantum Darwinism have demonstrated that, while a generic feature of quantum dynamics [13], it is nevertheless sensitive to seemingly small changes in the microscopic description [14,15], and non-Markovian effects can suppress the emergence of the phenomenon, although the relation between non-Markovianity and quantum Darwinism is yet to be fully understood [16][17][18][19][20][21]. Going beyond the single system particle, the proliferation of system information in spin registers interacting with spin [22] and boson [23] environments have shown to present different characteristics.…”