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Journal of Physics B Atomic Molecular and Optical Physics

Asymptotic dynamics of quantum discord in open quantum systems

K. Berrada, Hichem Eleuch, Y. Hassouni

Published Jul 6, 2011• 51 citations
Publisher

Abstract

It is well known that quantum entanglement makes certain tasks in quantum information theory possible. However, there are also quantum tasks that display a quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both practical and fundamental importance. Realistic quantum systems are not closed, and therefore it is important to study the various correlations when the system loses its coherence due to interactions with the environment. In this paper, we study in detail the dynamics of different kinds of correlations, classical correlation, quantum discord and entanglement in open quantum systems, in particular, a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, classical and quantum correlations can even persist asymptotically. By analytic and numerical analysis, we find that the quantum discord is larger than the classical correlation for asymptotic states. Furthermore, we show that the quantum discord is more resistant to the action of the environment than quantum entanglement, and it can persist even in the asymptotic long-time regime.

DOI
10.1088/0953-4075/44/14/145503

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It is well known that quantum entanglement makes certain tasks in quantum information theory possible. However, there are also quantum tasks that display a quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both practical and fundamental importance. Realistic quantum systems are not closed, and therefore it is important to study the various correlations when the system loses its coherence due to interactions with the environment. In this paper, we study in detail the dynamics of different kinds of correlations, classical correlation, quantum discord and entanglement in open quantum systems, in particular, a two-qubit system evolving under Kossakowski-type quantum dynamical semigroups of completely positive maps. In such an environment, classical and quantum correlations can even persist asymptotically. By analytic and numerical analysis, we find that the quantum discord is larger than the classical correlation for asymptotic states. Furthermore, we show that the quantum discord is more resistant to the action of the environment than quantum entanglement, and it can persist even in the asymptotic long-time regime.
Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system-environment dynamics of two-qubit quantum discord and the influence of initial system-environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.
Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system–environment dynamics of two-qubit quantum discord and the influence of initial system–environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of continuous variable quantum entanglement and quantum discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that discord decays asymptotically in time under the effect of the thermal bath. We describe also the time evolution of classical correlations.
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.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initially separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and we show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze time evolution of Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and we show that quantum discord decays asymptotically in time under the effect of thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of quantum system.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath. This is contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.