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Laser Physics Letters

Quantum estimation for Dirac particles with the Hawking effect in the background of a Schwarzschild black hole

Cheng‐Cheng Liu, Jiadong Shi, Zhiyong Ding, Juan He, Tao Wu, Liu Ye

Published Jul 9, 2019• 3 citations
Publisher

Abstract

Abstract In this paper, we analytically explore the effect of Hawking radiation on quantum Fisher information (QFI) for Dirac particles in the background of Schwarzschild black hole. What surprise us is that the Hawking radiation could not disturb QFI with respect to the state parameter ( ). Additionally, we also find in the case of an almost extreme black hole, or when the black hole is approximate to evaporating completely, QFI with respect to the Hawking temperature T ( ) always being zero indicates that the parameter estimation precision about the Hawking temperature is minimum in the two situations above. In particular, the maximal is obtained when the Hawking temperature is a fixed value for every state parameter . Furthermore, we investigate how the Hawking effect influences the distribution of the QFI over subsystems in physical accessible regions and find that QFI can be either subadditive or superadditive, depending on the specific parameter under the Hawking effect. At last, we also study the QFI of other possible bipartite divisions, which are physically inaccessible, and the nontrivial results reveal that QFI is averagely distributed in different physical regions.

DOI
10.1088/1612-202x/ab286c

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Abstract In this paper, we analytically explore the effect of Hawking radiation on quantum Fisher information (QFI) for Dirac particles in the background of Schwarzschild black hole. What surprise us is that the Hawking radiation could not disturb QFI with respect to the state parameter ( ). Additionally, we also find in the case of an almost extreme black hole, or when the black hole is approximate to evaporating completely, QFI with respect to the Hawking temperature T ( ) always being zero indicates that the parameter estimation precision about the Hawking temperature is minimum in the two situations above. In particular, the maximal is obtained when the Hawking temperature is a fixed value for every state parameter . Furthermore, we investigate how the Hawking effect influences the distribution of the QFI over subsystems in physical accessible regions and find that QFI can be either subadditive or superadditive, depending on the specific parameter under the Hawking effect. At last, we also study the QFI of other possible bipartite divisions, which are physically inaccessible, and the nontrivial results reveal that QFI is averagely distributed in different physical regions.
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.
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.
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.
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.
The genuine entanglement of Dirac fields for an N-partite system is investigated in Schwarzschild spacetime and the analysis is carried out using the single-mode approximation. Due to the Hawking effect, quantum entanglement is divided into two parts physically accessible and inaccessible entanglement. We obtain a general analytic expression of genuine N-partite entanglement that includes all accessible and inaccessible entanglement in a Schwarzschild black hole. Unlike bosonic entanglement, the accessible N-partite entanglement of Dirac fields monotonically decreases to a nonzero value with the Hawking temperature. Interestingly, the inaccessible N-partite entanglement is a monotonic or non-monotonic function of the Hawking temperature, depending on the ratio between accessible and inaccessible modes, in contrast to bipartite or tripartite entanglement that is only a monotonic function of the Hawking temperature. Finally, we obtain two restrictive relationships for the quantum information of the black hole. This conclusion provides a new understanding of Hawking effect of the black hole.
Abstract The black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.