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arXiv:1705.03185 · Laser Physics Letters

The enhancement of quantum entanglement under an open Dirac system with the Hawking effect in Schwarzschild space-time

Wen-Yang Sun, Dong Wang, Bao-Long Fang, Jia-Dong Shi, Liu Ye

Published May 10, 2018• 4 citations
arXivHTMLPDF

Abstract

Abstract In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.

DOI
10.1088/1612-202x/aab69c

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Abstract In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.
Abstract Quantum entanglement is a key resource for quantum communication protocols such as quantum cryptography, quantum key distribution (QKD), and quantum secret sharing (QSS), but interactions with the environment can degrade entanglement through decoherence. In this work, weak measurement and post-noise filtration are employed to mitigate entanglement degradation in a tripartite system of entangled Dirac particles interacting with a generalised amplitude damping (GAD) channel and the Hawking radiation associated with a Schwarzschild black hole. Particles A and B are subjected to the GAD channel, whereas particle C is influenced by the Schwarzschild background. The logarithmic negativity is evaluated for the bipartitions A|BC 1 and C 1 |AB. The results show that weak measurement combined with post-noise filtration can enhance the conditional entanglement retained by the system. This enhancement, however, can be accompanied by a reduction in the conditional filtration success probability and the corresponding weighted entanglement yield. Under the parameter regimes considered, the C 1 |AB bipartition exhibits a larger relative entanglement enhancement than the A|BC 1 bipartition.
We explore the performance of various correlation measures for open Dirac system with Hawking effect in Schwarzschild space–time. Our results indicate that the impact of Hawking effect on physical accessible entanglement is weaker than that of decoherence. For generalized amplitude damping (GAD) channel, the entanglement sudden death (ESD) is analyzed in detail, and the inequivalence of quantization for Dirac particles in the black hole and Kruskal space–time is verified via quantum discord measure. In addition, as an example for interpreting Bell non-locality, we study the GAD channel with Hawking effect. It can be noticed that there is a boundary line of Bell violation for physically accessible states. That is, quantum non-locality would disappear when Hawking temperature exceeds a certain value. This critical temperature increases as a decoherence parameter decreases. In the case of phase damping (PD) channel, the interaction between the particle and noise environment does not produce bipartite system–environment entanglement. Then we discuss entanglement distributions, and find that the reduced physically accessible entanglement can be redistributed to physical inaccessible region. At last, we extend our investigation to an N-qubit system, and obtain a universal expression of the physical accessible entanglement.
In this paper, the effect of Hawking radiation on the multipartite entanglement of Dirac particles in the background of a Schwarzschild black hole is investigated. It is shown that all the 1-tangles decrease as the Hawking temperature grows, and the Coffman--Kundu--Wootters monogamy inequality is always saturated in this system. It is also shown that the entanglement's status of subsystems, which have the same quantum state, depend on its detector's position, and this proposition can be generalized to a multipartite system. Then, we find that the Hawking effect does not change the entanglement structure of the quantum state in Schwarzschild space-time. In addition, we discuss the distributions of quantum information and find that not only is the entanglement redistributed, but also the mutual information is distributed to the physical inaccessible region. At last, we calculate the mutual information of a NNN-qubit multipartite system, ${|\mathrm{\ensuremath{\Psi}}⟩}_{123\dots{}N}={(\ensuremath{\beta}{|0⟩}^{\ensuremath{\bigotimes}N}+\sqrt{1\ensuremath{-}{\ensuremath{\beta}}^{2}}{|1⟩}^{\ensuremath{\bigotimes}N})}_{123\dots{}N}$, and draw a conclusion that when the black hole approximates to evaporate completely the mutual information of this system will be close to $(N\ensuremath{-}1)/N$ of the original if a particle freely falls in toward a Schwarzschild black hole and locates near the event horizon, and the other particles remain in the asymptotically flat region.
Abstract The unavoidable interaction of a real quantum system with the environment leads to the degradation of quantum coherence. Consequently, this paper investigates how such interaction can influence the quantum Fisher information (QFI) with the Hawking effect in the Schwarzschild black hole. We have considered two models of quantum decoherence: amplitude damping and phase damping channels; both can be experimentally induced. We found that Quantum information F ϕ is more robust to phase flip channel than to the amplitude damping channel. It is observed that under the influence of phase damping channel, Quantum information F θ does not depend on Hawking temperature making the parameter estimation immune to the Hawking effect but susceptible to decoherence. We found that QFI dwindles with increasing Hawking temperature and becomes more attenuated with decoherence which implies that the parameter estimation can be achieved with higher precision when the black hole is not evaporating.
Previous studies have shown that the decoherence of environments generally negatively influences the quantum correlations in the Schwarzschild black hole . In our paper, we find that the decoherence of the generalized amplitude damping (GAD) channel has both positive and negative effects on the quantum coherence of Dirac fields, which means that the decoherence of environments can not only reduce the quantum coherence but also increase the quantum coherence in Schwarzschild spacetime. This result banishes the widespread belief that the decoherence of the environment can only destroy the quantum coherence in curved spacetime. Furthermore, another novel phenomenon has been observed for the first time: with increasing Hawking temperature T, the QFI of physically inaccessible modes rapidly decays from infinity to 0, which may provide a way to detect whether the particles enter the physically inaccessible region or not. This result may provide a new perspective for exploring and analyzing black holes.
Abstract The merging of quantum information science with the relativity theory presents novel opportunities for understanding the enigmas surrounding the transmission of information in relation to black holes. For this purpose, we study the quantumness near a Schwarzschild black hole in a practical model under decoherence. The scenario we consider in this paper is that a stationary particle in the flat region interacts with its surroundings while another particle experiences free fall in the vicinity of a Schwarzschild black hole’s event horizon. We explore the impacts of Hawking radiation and decoherence on the system under investigation and find that these effects can limit the survival of quantum characteristics, but cannot destroy them completely. Hence, the results of this study possess the potential to yield valuable insights into the comprehension of the quantum properties of a real system operating within a curved space-time framework.