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Chinese Physics B

Dynamics of quantum discord in a two-qubit system under classical noise

You-neng Guo, Mao-Fa Fang, Xiang Liu, Bai-Yuan Yang

Published Mar 1, 2014• 5 citations
Publisher

Abstract

We study the quantum discord dynamics of two noninteracting qubits that are, respectively, subject to classical noise. The results show that the dynamics of quantum discord are dependent on both the coupling between the qubits and classical noise, and the average switching rate of the classical noise. In the weak-coupling Markovian region, quantum discord exhibits exponent decay without revival, and can be well protected by increasing the average classical noise switching rate. While in the strong-coupling non-Markovian region, quantum discord reveals slowly decayed oscillations with quick revival by decreasing the average switching rate of the classical noise. Thus, our results provide a new method of protecting quantum discord in a two-qubit system by controlling the coupling between the qubits and classical noise, and the average switching rate of the classical noise.

DOI
10.1088/1674-1056/23/3/034204

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We study the quantum discord dynamics of two noninteracting qubits that are, respectively, subject to classical noise. The results show that the dynamics of quantum discord are dependent on both the coupling between the qubits and classical noise, and the average switching rate of the classical noise. In the weak-coupling Markovian region, quantum discord exhibits exponent decay without revival, and can be well protected by increasing the average classical noise switching rate. While in the strong-coupling non-Markovian region, quantum discord reveals slowly decayed oscillations with quick revival by decreasing the average switching rate of the classical noise. Thus, our results provide a new method of protecting quantum discord in a two-qubit system by controlling the coupling between the qubits and classical noise, and the average switching rate of the classical noise.
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.
Abstract Exploring strategies to protect quantum correlations from the detrimental effects of their surroundings is crucial in the field of quantum computing and information sciences. For this purpose, we consider a simple engineered environment consisting of two noninteracting separated qubits, each embedded in a single-mode lossy cavity which is further connected to another lossy cavity. We investigate the dynamics and protection of quantum discord for the initially maximum entangled state in the weak and strong coupling regimes between the qubits and their corresponding cavities. It is found that the quantum discord can be preserved efficiently for a much longer time by adjusting the hopping strengths between the two coupled cavities. In addition, if the secondary cavity is perfect then a stationary quantum discord between the two qubits arises after certain damping oscillations. Interestingly, the magnitude of the stationary quantum discord can be maximized by increasing the coupling strengths of the two cavities.
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 address the dynamics of entanglement and quantum discord for two noninteracting qubits initially prepared in a maximally entangled state and then subjected to a classical colored noise, i.e., coupled with an external environment characterized by a noise spectrum of the form $1/{f}^{\ensuremath{\alpha}}$. More specifically, we address systems in which the Gaussian approximation fails, i.e., mere knowledge of the spectrum is not enough to determine the dynamics of quantum correlations. We thus investigate the dynamics for two different configurations of the environment: in the first case, the noise spectrum is due to the interaction of each qubit with a single bistable fluctuator with an undetermined switching rate, whereas in the second case we consider a collection of classical fluctuators with fixed switching rates. In both cases, we found analytical expressions for the time dependence of entanglement and quantum discord, which may also be extended to a collection of fluctuators with random switching rates. The environmental noise is introduced by means of stochastic time-dependent terms in the Hamiltonian, and this allows us to describe the effects of both separate and common environments. We show that the non-Gaussian character of the noise may lead to significant effects, e.g., environments with the same power spectrum, but different configurations give rise to the opposite behavior for quantum correlations. In particular, depending on the characteristics of the environmental noise considered, both entanglement and discord display either a monotonic decay or the phenomena of sudden death and revivals. Our results show that the microscopic structure of the environment, in addition to its noise spectrum, is relevant for the dynamics of quantum correlations and may be a valid starting point for the engineering of non-Gaussian colored environments.
The non-Markovian decoherence of quantum and classical correlations is analytically obtained when two qubits are asymmetrically subjected to the bit flip channel and phase flip channel. For one class of initial mixed states, quantum correlations quantified by quantum discord decay synchronously with classical correlations. The discovery that the decaying rates of quantum and classical correlations suddenly change at the characteristic time is physically interpreted by the distance from quantum state to the closest classical states. In a large time interval, quantum correlations are greater than classical correlations. The quantum and classical correlations can be preserved over a longer period of time via the kernel characterizing the environment memory effects.
The dissipative dynamics of classical correlation(CC), quantum discord(QD) and entanglement (QE) of two qubits in two-side and one-side decoherence models are inves- tigated under Markovian environments. We find the sudden change QD as well as CC and sudden death of entanglement (ESD). The results show that QD and QE decay faster with the increasing of squeezing parameter r; the dipole-dipole interaction W under two-side decoherence leads to the oscillation of quantum discord and concurrence for initial non- eigenstates; while in all cases when entanglement suddenly disappears, quantum discord keeps nonzero under same conditions.