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Chinese Physics B

Effects of classical random external field on the dynamics of entanglement in a four-qubit system

Edwige Carole Fosso, Fridolin Tchangnwa Nya, Lionel Tenemeza Kenfack, Martin Tchoffo

Published Jun 16, 2021• 1 citation
Publisher

Abstract

We investigate the dynamics of entanglement through negativity and witness operators in a system of four non-interacting qubits driven by a classical phase noisy laser characterized by a classical random external field (CREF). The qubits are initially prepared in the GHZ-type and W-type states and interact with the CREF in two different qubit-field configurations, namely, common environment and independent environments in which the cases of equal and different field phase probabilities are distinguished. We find that entanglement exhibits different decaying behavior, depending on the input states of the qubits, the qubit-field coupling configuration, and field phase probabilities. On the one hand, we demonstrate that the coupling of the qubits in a common environment is an alternative and more efficient strategy to completely shield the system from the detrimental impacts of the decoherence process induced by a CREF, independent of the input state and the field phase probabilities considered. Also, we show that GHZ-type states have strong dynamics under CREF as compared to W-type states. On the other hand, we demonstrate that in the model investigated the system robustness’s can be greatly improved by increasing the number of qubits constituting the system.

DOI
10.1088/1674-1056/ac0bab

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We investigate the dynamics of entanglement through negativity and witness operators in a system of four non-interacting qubits driven by a classical phase noisy laser characterized by a classical random external field (CREF). The qubits are initially prepared in the GHZ-type and W-type states and interact with the CREF in two different qubit-field configurations, namely, common environment and independent environments in which the cases of equal and different field phase probabilities are distinguished. We find that entanglement exhibits different decaying behavior, depending on the input states of the qubits, the qubit-field coupling configuration, and field phase probabilities. On the one hand, we demonstrate that the coupling of the qubits in a common environment is an alternative and more efficient strategy to completely shield the system from the detrimental impacts of the decoherence process induced by a CREF, independent of the input state and the field phase probabilities considered. Also, we show that GHZ-type states have strong dynamics under CREF as compared to W-type states. On the other hand, we demonstrate that in the model investigated the system robustness’s can be greatly improved by increasing the number of qubits constituting the system.
Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and [Formula: see text]-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the [Formula: see text]-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.
In this paper, we exploit the notions of tripartite quantum discord , tripartite negativity , and entanglement witnesses (EWs), respectively, as a measure of quantum correlations in a model of three noninteracting qubits subject to a classical random external field. We compare the dynamics of with that of entanglement for the initial entangled pure or mixed GHZ- and W-type states. We find that the quantum correlations dynamics depend on the input configuration of the purity of the initial states. The results show that may be more robust than entanglement and no sudden death of the occurs, whereas entanglement displays periodically sudden death and revivals in the regions for GHZ- and W-type states driven by a classical random external field. Furthermore, we also show that the survival partial entanglement can be detected by means of the suitable EWs.
The paper investigates the dynamics of entanglement and explores some geometrical characteristics of the trajectories in state space, in four-qubit Greenberger-Horne-Zeilinger (GHZ)-and W-type states, coupled to common and independent classical random telegraph noise (RTN) sources. It is shown from numerical simulations that: (i) the dynamics of entanglement depends drastically not only on the input configuration of the qubits and the presence or absence of memory effects, but also on whether the qubits are coupled to the RTN in a CE or IEs; (ii) a considerable amount of entanglement can be indefinitely trapped when the qubits are embedded in a CE; (iii) the CE configuration preserve better the entanglement initially shared between the qubits than the IEs, however, for W-type states, there is a period of time and/or certain values of the purity for which, the opposite can be found. Thanks to results obtained in our earlier works on the three-qubit model, we are able to conclude that entanglement becomes more robustly protected from decay when the number of qubits of the system increases. Finally, we find that the trajectories in state space of the system quantified by the quantum Jensen Shannon divergence (QJSD) between the time-evolved states of the qubits and some reference states may be curvilinear or chaotic.
In the present paper, the joint effects of two kinds of classical environmental noises, without direct interaction among each other, on the dynamics of quantum correlations (QCs) of a three-qubit system coupled in independent environments is investigated. More precisely, we join the random telegraph noise (RTN) and the static noise (SN) and focus on the dynamics of entanglement and quantum discord (QD) when the qubits are initially prepared in the GHZ- and W-type states. The overall noise affecting the qubits is obtained by combining the RTN and SN in two different setups. The results show that the disorder of the environmental noise as well as its memory qualities and the purity of the initial state considered play a crucial role in the time evolution of the system in such a way that the dynamics of QCs can be controlled by varying them. In fact, we show that, depending on the initial state and noise regime considered, the rate of collapse of QCs may either decrease or increase with the increase of the degree of disorder of the SN, the switching rate of the RTN and the purity of the initial state.
We study the evolution of entanglement and nonlocality of a non-interacting qubit-qutrit system under the effect of random telegraph noise (RTN) in independent and common environments in Markovian and non-Markovian regimes. We investigate the dynamics of qubit-qutrit system for different initial states. These systems could be existed in far astronomical objects. A monotone decay of the nonlocality (entanglement) is found in the Markov regime, while for non-Markovian noise, phenomena of sudden change (death) and revival occurs. We find that the preserving nonlocality (entanglement) depends on initial state of the system in common and independent environments; so, we can not strictly conclude that independent or common environments are more robust against the noise.
Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies. In this regard, we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent (Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field. Then, we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure. It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency, the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies (central detuning) in both non-Markovian and Markovian reservoirs. While the central detuning has a constructive role, the detuning between the qubit and the classical field (laser detuning) affects negatively on the entanglement protection. The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir. We demonstrate that, in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.