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Laser Physics Letters

Exploration of quantum correlations in an open system with Unruh effect under a Schwarzschild space-time

Wen‐Yang Sun, Jiaojiao Chen, A-Min Ding, Dong Wang, Liu Ye

Published Oct 17, 2019• 3 citations
Publisher

Abstract

Abstract In this letter, we investigate quantum correlations (quantum discord, concurrence and Bell nonlocality) in an open system (amplitude damping channel) with the Unruh effect under a Schwarzschild space-time. In an amplitude damping (AD) channel, we can discover that the Hawking–Unruh effects and decoherence will influence these quantum correlations. However, quantum correlations always decrease with increasing the AD decoherence strength, irrespective of whether there are Hawking–Unruh effects. The results also indicate that the impact of the AD decoherence on quantum correlations is stronger than that of the Hawking–Unruh effects. Besides, we find that if concurrence is present, Bell nonlocality may disappear. This means that the Bell nonlocal states are a strict subset of the entangled states. Furthermore, the redistributions of quantum correlations are discussed in detail under a Schwarzschild space-time. The results show that the reduced physically accessible quantum correlations can be redistributed to the physically inaccessible regions.

DOI
10.1088/1612-202x/ab4994

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Physics Letters B•Mar 13, 2026•1 citation
Abstract In this letter, we investigate quantum correlations (quantum discord, concurrence and Bell nonlocality) in an open system (amplitude damping channel) with the Unruh effect under a Schwarzschild space-time. In an amplitude damping (AD) channel, we can discover that the Hawking–Unruh effects and decoherence will influence these quantum correlations. However, quantum correlations always decrease with increasing the AD decoherence strength, irrespective of whether there are Hawking–Unruh effects. The results also indicate that the impact of the AD decoherence on quantum correlations is stronger than that of the Hawking–Unruh effects. Besides, we find that if concurrence is present, Bell nonlocality may disappear. This means that the Bell nonlocal states are a strict subset of the entangled states. Furthermore, the redistributions of quantum correlations are discussed in detail under a Schwarzschild space-time. The results show that the reduced physically accessible quantum correlations can be redistributed to the physically inaccessible regions.
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 Letter, we analytically explore the effect of the Hawking radiation on the quantum correlation and Bell non-locality for Dirac particles in the background of Schwarzschild black hole. It is shown that when the Hawking effect is almost nonexistent, corresponding to the case of an almost extreme black hole, the quantum properties of physically accessible state are the same for the initial situation. For finite Hawking temperature T, the accessible quantum correlation monotonously decreases along with increasing T owing to the thermal fields generated by the Hawking effect, and the accessible quantum non-locality will be disappeared when the Hawking temperature is more than a fixed value which increases with the parameter r of Werner state growing. Then we analyze the redistribution of quantum correlation, and find that for the case of the Hawking temperature being infinite, corresponding to the case of the black hole evaporating completely, the quantum correlation of physically accessible state is equal to the one of the inaccessible states. Moreover, due to the Pauli exclusion principle and the differences between Fermi–Dirac and Bose–Einstein statistics, for the Dirac fields the accessible classical correlation decreases with increase of the Hawking temperature, which is different for the scalar fields. For Bell non-locality, we also find that the quantum non-locality is always extinct for physically inaccessible states, and the strength of the non-locality decreases with enlarging intensity of Hawking effect when the non-locality is existent in physically accessible state.
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.
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 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.
Recent progress suggests that Hawking radiation originates not from the black hole’s event horizon but from a quantum atmosphere outside the horizon. Consider this, the current work focuses on revealing the effect of the quantum atmosphere on various quantum resources in the Schwarzschild black hole, including nonlocal advantage of quantum coherence (NAQC), Bell nonlocality, quantum steering, and quantum discord (QD). Interestingly, it is found that the quantumness of the accessible region is strongest near the event horizon, and will decline as the particle is far away from it. Furthermore, the hierarchical relationship among the concerned quantum resources are shown, i.e., the NAQC represent a stronger quantum correlation compared to quantum steering and Bell nonlocality, implying that a bipartite state achieving NAQC must also be steerable and Bell nonlocal. Additionally, we examine the monogamy relation of quantum discord in the quantum atmosphere framework. It turns out that the squared quantum discord (SQD) is monogamous, whereas quantum discord (QD) is not. Furthermore, it is verified that the bipartite QD constrains the sum of SQD in physically accessible and inaccessible regions. This current study sheds light on the quantumness in quantum atmosphere, and facilitate us understand information paradox of black holes from the viewpoint of quantum resource theories.