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Multipartite quantum correlations and coherence dynamics subjected to classical environments and fractional Gaussian noise

Atta Ur Rahman, Muhammad Javed, Lionel Tenemeza Kenfack, Khan, Salman

Published Jan 1, 2021• 2 citations
Publisher

Abstract

We address the dynamical map of entanglement and coherence in a four qubit maximally entangled GHZ states coupled with classical environments driven by fractional Gaussian noise. The system-environment coupling is assumed in four different schemes: common, bipartite, tripartite, and independent system-environment configuration. We show that entanglement preservation can be modeled in multipartite GHZ-like states using parameter optimization in the current local environments except for the independent configuration. The decay is characterized by monotonous functions in time and the exact fluctuating behaviour of the local fields, as well as entanglement sudden death and birth revivals, are completely suppressed. Not only noise, but also the nature of qubit-environment coupling and the number of independent environments coupled, have dephasing effects on the entanglement and coherence preservation. Furthermore, as the Hurst parameter of fractional Gaussian noise is increased, the decay becomes delayed initially. Finally, the four-qubit GHZ state is found to be a good resource for quantum information processing that can withstand noise dissipation, particularly under a common noise source.

DOI
10.13140/rg.2.2.12689.35688

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We address the dynamical map of entanglement and coherence in a four qubit maximally entangled GHZ states coupled with classical environments driven by fractional Gaussian noise. The system-environment coupling is assumed in four different schemes: common, bipartite, tripartite, and independent system-environment configuration. We show that entanglement preservation can be modeled in multipartite GHZ-like states using parameter optimization in the current local environments except for the independent configuration. The decay is characterized by monotonous functions in time and the exact fluctuating behaviour of the local fields, as well as entanglement sudden death and birth revivals, are completely suppressed. Not only noise, but also the nature of qubit-environment coupling and the number of independent environments coupled, have dephasing effects on the entanglement and coherence preservation. Furthermore, as the Hurst parameter of fractional Gaussian noise is increased, the decay becomes delayed initially. Finally, the four-qubit GHZ state is found to be a good resource for quantum information processing that can withstand noise dissipation, particularly under a common noise source.
The dynamical map of entanglement and mixedness in four-qubit maximally entangled GHZ state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement and purity preservation may be simulated in multipartite GHZ-like states. Quantum correlations and purity decrease exponentially in four qubits, and exact fluctuating local field behaviour, as well as entanglement sudden death and birth revivals, are completely suppressed. Entanglement and purity preservation are affected by noise and the number of independent channels utilised. The Hurst parameter of fractional Gaussian noise was discovered in the four qubits to improve entanglement and avoid mixedness. Different entanglement and mixedness criteria yield different results, emphasizing the need to investigate various approaches in order to uncover multipartite correlations.
Abstract We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein–Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure exponential decay of a considerable amount. The current Markovian dynamical map, as well as suppression of the fluctuating character of the environments, are observed to be entirely attributable to the Gaussian nature of the noise. The increasing number of environments are witnessed to speed up the amount of decay. Unlike other noises, the current noise parameter’s flexible range is readily exploitable, ensuring long enough preserved memory properties. The four-qubit GHZ state, besides having a large information storage potential, stands partially entangled and coherent in common environments for an indefinite duration. In addition, we derive computational values for each system-environment interaction, which will help quantum practitioners to optimize the related classical 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.
The ability to preserve multipartite entanglement in noisy environments is central to advancing quantum information processing. In this work, we develop a semiclassical theoretical model of three entangled qubits exposed to local Markov noise environments with tunable statistical correlations between noise sources. We show that such correlations can significantly influence the dynamics of multipartite entanglement, in some cases slowing its decay and, under ideal conditions, even enabling full preservation. Using tripartite negativity as an entanglement measure, we derive analytical results for the GHZ and W states, demonstrating their contrasting responses to correlated and anticorrelated noise. Our analysis identifies regimes in which multipartite entanglement can be sustained despite environmental interactions, offering new insight into how noise correlations may serve as a resource for protecting quantum coherence in multi-qubit systems.
We address the dynamics of a two-qubit system interacting with a classical dephasing environment driven by a Gaussian stochastic process. Upon introducing the concept of entanglement-preserving time, we compare the degrading effects of different environments, e.g. those described by Ornstein–Uhlenbeck (OU) or fractional noise. In particular, we consider pure Bell states and mixtures of Bell states and study the typical values of the entanglement-preserving time for both independent and common environments. We found that engineering environments towards fractional Gaussian noise is useful to preserve entanglement as well as to improve its robustness against noise. We also address entanglement sudden death by studying the sudden-death time as a function of the initial negativity. We found that: (i) the sudden-death time is bounded from below by an increasing function of the initial negativity, (ii) the sudden-death time depends only slightly on the process used to describe the environment and exhibits typicality. Overall, our results show that engineering the environment has only a slight influence over the entanglement sudden-death time, while it represents a valuable resource to increase the entanglement-preserving time, i.e. to maintain entanglement closer to the initial level for a longer interaction time.
Many-qubit entanglement is crucial for quantum information processing although its exploitation is hindered by the detrimental effects of the environment surrounding the many-qubit system. It is thus of importance to study the dynamics of general multipartite non-classical correlation, including but not restricted to entanglement, under noise. We did this study for four-qubit Greenberger–Horne–Zeilinga (GHZ) state under most common noises in an experiment and found that non-classical correlation is more robust than entanglement except when it is imposed to dephasing channel. Quantum discord presents a sudden transition in its dynamics for Pauli-X and Pauli-Y noises as well as Bell-diagonal states interacting with dephasing reservoirs and it decays monotonically for Pauli-Z and isotropic noises.