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arXiv:1407.3225 · Physical Review A

Role of entanglement for nonlocal memory effects

Steffen Wißmann, Heinz‐Peter Breuer

Published Sep 30, 2014• 8 citations
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Abstract

We determine the role of entanglement for nonlocal memory effects induced by initial correlations in a composite environment. The dephasing dynamics of two two-level systems which are coupled locally to an environment consisting of nonlocally correlated field modes is studied with respect to the occurrence of reviving nonlocal coherences. Employing two-mode Gaussian states correlating pairs of modes of the bosonic baths we observe strong nonlocal memory effects in this locally Markovian dynamics for entangled as well as separable quantum states for the environment. We present an explanation for this phenomenon linking it to the correlation coefficient of the environmental coupling operators and derive a necessary and sufficient condition for the occurrence of nonlocal memory effects for sufficiently short interaction times. Finally, we comment on how the magnitude of the nonlocal rephasing may also be used to estimate parameters of the two-mode Gaussian states.

DOI
10.1103/physreva.90.032117

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We determine the role of entanglement for nonlocal memory effects induced by initial correlations in a composite environment. The dephasing dynamics of two two-level systems which are coupled locally to an environment consisting of nonlocally correlated field modes is studied with respect to the occurrence of reviving nonlocal coherences. Employing two-mode Gaussian states correlating pairs of modes of the bosonic baths we observe strong nonlocal memory effects in this locally Markovian dynamics for entangled as well as separable quantum states for the environment. We present an explanation for this phenomenon linking it to the correlation coefficient of the environmental coupling operators and derive a necessary and sufficient condition for the occurrence of nonlocal memory effects for sufficiently short interaction times. Finally, we comment on how the magnitude of the nonlocal rephasing may also be used to estimate parameters of the two-mode Gaussian states.
We explore the possibility to generate nonlocal dynamical maps of an open quantum system through local system-environment interactions. Employing a generic decoherence process induced by a local interaction Hamiltonian, we show that initial correlations in a composite environment can lead to nonlocal open system dynamics which exhibit strong memory effects, although the local dynamics is Markovian. In a model of two entangled photons interacting with two dephasing environments, we find a direct connection between the degree of memory effects and the amount of correlation in the initial environmental state. The results demonstrate that, contrary to conventional wisdom, enlarging an open system can change the dynamics from Markovian to non-Markovian.
Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.
We investigate the preservation and dynamics of entanglement and Bell nonlocality in a two-photon system subject to local dephasing, particularly emphasizing environments exhibiting non-Markovian memory effects. By analyzing the interplay between entanglement, as measured by concurrence, and Bell inequality violation, we identify time regions where Bell inequality is not violated, even when concurrence remains high. This indicates that strongly entangled states do not always exhibit nonclassical correlations with certainty. Our study further explores the effects of refractive index variations, spectral width, and interaction symmetry, demonstrating how structured environments and controlled environmental interactions can mitigate decoherence and enhance the resilience of quantum correlations. We propose that these theoretical predictions can be tested using modifications of recent experimental optical setups. These findings provide valuable insights into the conditions under which quantum correlations remain irreproducible by classical local hidden-variable models, with direct implications for quantum communication, quantum information processing, and foundational studies in quantum mechanics. Furthermore, our findings highlight the crucial importance of quantum coherence in maintaining entanglement and nonlocality over extended time evolution. These results show remarkable alignment with the experimental observations, demonstrating high accuracy and consistency within the expected parameter range.
We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian–non-Markovian (both of the two local dynamics are non-Markovian) or Markovian–non-Markovian, but not under the condition of Markovian–Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian–Markovian. It shows that the function of correlations between two environments has an upper bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration, we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects.
In this work, we study the effects of different forms of correlations of environments on the dynamics of open systems’ entanglement and discord. We consider two two-level atoms A and B interacting, respectively with two spatially separated modes a and b, each of which is in turn surrounded by a dissipative reservoir. The two modes may initially be in an entangled or classically correlated or product state with their marginal state being the same in all the cases. We compare the power of different environmental correlation forms in the revival of the atoms’ entanglement and discord in the strong atom–mode coupling regime. We also show how the dynamical behavior of the atoms’ entanglement and discord nontrivially change by the presence of initial environmental correlation in the weak atom–mode coupling regime. Finally, we reveal that initial entanglement between the modes can induce correlations between initially uncorrelated atoms.