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Non-classical Correlations of Accelerated Observers Interacting with a Classical Stochastic Noise

Mahmoud Youssef Abd‐Rabbou, Mahmood Shamirzaie, Salman Naeem Khan

Published Jan 17, 2023• 0 citations
Publisher

Abstract

Abstract The influence of a classical environment on the behaviour of the Wigner function and the concurrence of an accelerated two-qubit system interacting is discussed. The negative values of the Wigner function verify the non-classicality, while the concurrence shows the entanglement degree of the quantum system. We assume one or both observers are accelerated (s) and interact with a common or independent environment. Suppression of the coherence rises due to acceleration effect, noise strength, and noise frequency are pointed. The amount of quantum entanglement is investigated by using the quantum concurrence, where its positive values are consistent with what the negative Wigner function shows. We found that the degradation of coherence of the initial system reduces when observers interact with their environments independently more than when it interacts with a common one. It is also sensitive to the acceleration status of both observers. Additionally, the correlation and entanglement pertinent to the situation with common or independent noise agents behave contrarily for the two regimes of Markovian and non-Markovian noises.

DOI
10.21203/rs.3.rs-2479176/v1

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Abstract The influence of a classical environment on the behaviour of the Wigner function and the concurrence of an accelerated two-qubit system interacting is discussed. The negative values of the Wigner function verify the non-classicality, while the concurrence shows the entanglement degree of the quantum system. We assume one or both observers are accelerated (s) and interact with a common or independent environment. Suppression of the coherence rises due to acceleration effect, noise strength, and noise frequency are pointed. The amount of quantum entanglement is investigated by using the quantum concurrence, where its positive values are consistent with what the negative Wigner function shows. We found that the degradation of coherence of the initial system reduces when observers interact with their environments independently more than when it interacts with a common one. It is also sensitive to the acceleration status of both observers. Additionally, the correlation and entanglement pertinent to the situation with common or independent noise agents behave contrarily for the two regimes of Markovian and non-Markovian noises.
Abstract This paper investigates the behaviour of the quantum correlations for an accelerated two-qubit system during its interaction with a classical stochastic field, utilizing the Wigner function and concurrence. The non-classical behaviour is indicated by negative values of the Wigner function, while the degree of entanglement is demonstrated by the concurrence. To consider acceleration and interaction with a common or independent environment, we discard the single-mode approximation and utilize the Unruh construction of the quantum field mode in our analysis. Our results suggest that coherence suppression is caused by the acceleration effect, noise strength, and noise frequency. Through an examination of quantum concurrence, this study analyses the level of quantum entanglement that corresponds positively with negative values of the Wigner function. The findings indicate that coherence degradation in the initial system is reduced when observers interact independently with their environments, as opposed to interacting with a common environment. Additionally, the acceleration of both observers has an impact on coherence reduction. During system evolution, the Wigner function displays collapse and reappearance behaviour, while quantum entanglement undergoes local collapse and revival phenomena. Notably, common noise situations exhibit more rapid variation in both the Wigner function and entanglement compared to independent noise configurations.
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
Abstract We address the time evolution of quantum correlations (QCs) such as entanglement, purity, and coherence for a model of two non-interacting qubits initially prepared as a maximally entangled bipartite state. We contrast the comparative potential of the classical fields to preserve these QCs in the noisy and noiseless realms. We also disclose the characteristic dynamical behavior of the QCs of the two-qubit state under the static noise effects originating from the common and different configuration models. We show that there is a direct connection between the fluctuations allowed by an environment and the preservation of QCs. Due to the static noise dephasing effects, the QCs are suppressed, resulting in the separability of the two-qubit entangled state after a finite duration. For bipartite QCs preservation, we show that the common configuration is more resourceful than the different configuration. Furthermore, this protection of the QCs under static noise for large intervals is entirely attributable to the existence of the entanglement sudden death and birth phenomenon. Most importantly, we found the bipartite QCs less fragile than the tripartite ones in comparison under the static noise. In addition, we find the concurrence measure to show more evident revivals of entanglement in comparison.
We analyze the effect of a classical noise into the entanglement dynamics between two particles, initially entangled, subject to continuous time quantum walks in a one-dimensional lattice. The noise is modeled by randomizing the transition amplitudes from one site to another. Both Markovian and non-Markovian environments are considered. For the Markov regime an exponential decay of the initial quantum correlation is found, while the loss of coherence of the quantum state increases monotonically with time up to a saturation value depending upon the degrees of freedom of the system. For the non-Markov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is found or deduced depending on the peculiar characteristics of the noise. Our results indicate that the entanglement dynamics in the non-Markovian regime is affected by the persistence of the memory effects of the environment and by its intrinsic features.
We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.
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.