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Laser Physics Letters

Quantum nonlocality phenomena in scalar and Dirac fields near a Schwarzschild black hole

Wen‐Yang Sun, Wenchao Ma, Dong Wang, Liu Ye

Published Jun 10, 2024• 1 citation
Publisher

Abstract

Abstract In this work, we explore the impact of the Hawking effect on quantum nonlocality, specifically the maximum violation of the Bell-CHSH inequality, for both scalar and Dirac fields within Schwarzschild spacetime. We reveal the nuanced behavior of the Bell-CHSH inequality as the Hawking temperature (HT) varies. For scalar fields, we observe distinct degradation patterns in the Bell-CHSH inequality, influenced by the state parameter α and its normalized counterpart 1 − α 2 . In contrast, Dirac fields exhibit two distinct degradation trajectories, each converging to different nonzero minimum values as HT approaches infinity T → ∞ , however, this does not apply to the maximally entangled state. Remarkably, the maximum violation of Bell-CHSH inequality becomes zero for scalar fields at infinite HT, while it stabilizes at a finite nonzero value for Dirac fields. Additionally, the quantum nonlocality robustness of the Dirac fields is stronger than that of the scalar fields. Therefore, this study enhances our understanding of the dynamic characteristics of nonlocality within scalar and Dirac fields near a Schwarzschild black hole.

DOI
10.1088/1612-202x/ad4eb5

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Abstract In this work, we explore the impact of the Hawking effect on quantum nonlocality, specifically the maximum violation of the Bell-CHSH inequality, for both scalar and Dirac fields within Schwarzschild spacetime. We reveal the nuanced behavior of the Bell-CHSH inequality as the Hawking temperature (HT) varies. For scalar fields, we observe distinct degradation patterns in the Bell-CHSH inequality, influenced by the state parameter α and its normalized counterpart 1 − α 2 . In contrast, Dirac fields exhibit two distinct degradation trajectories, each converging to different nonzero minimum values as HT approaches infinity T → ∞ , however, this does not apply to the maximally entangled state. Remarkably, the maximum violation of Bell-CHSH inequality becomes zero for scalar fields at infinite HT, while it stabilizes at a finite nonzero value for Dirac fields. Additionally, the quantum nonlocality robustness of the Dirac fields is stronger than that of the scalar fields. Therefore, this study enhances our understanding of the dynamic characteristics of nonlocality within scalar and Dirac fields near a Schwarzschild black hole.
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 We investigate how the Hawking effect reshapes distinct quantum resources of Dirac fields in Schwarzschild spacetime beyond the single-mode approximation. By quantifying quantum entanglement and coherence using the negativity, the l 1 -norm of coherence and the relative entropy of coherence, we observe a significant asymmetry in their response to gravitational effects. While the Hawking effect monotonically degrades entanglement and drives it toward a finite residual value, quantum coherence is instead monotonically amplified with increasing Hawking temperature, revealing the black hole as an effective decohering environment for nonlocal correlations but a coherence-enhancing mechanism for local superposition. Notably, we further find that under the influence of the Hawking effect, the maximally entangled state does not necessarily correspond to the largest initial negativity. In fact, its value may even be smaller than that of certain non-maximally entangled states. Our results demonstrate that gravity acts in a highly nonuniform manner on different facets of quantumness and highlight the necessity of resource-adapted state engineering for relativistic quantum information processing near the event horizon 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.
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.
We investigate bipartite quantum correlations of Dirac fields in the spacetime of a Hayward regular black hole. Using the Wootters concurrence and the CHSH Bell parameter, we analyze the influence of Hawking radiation on an entangled state shared by an inertial observer and a near-horizon observer. We show that, unlike the bosonic case, fermionic correlations remain nonzero even in the infinite-temperature limit owing to the Pauli exclusion principle, while part of the entanglement is redistributed to inaccessible modes inside the horizon. The accessible modes exhibit Bell nonlocality for all finite Hawking temperatures, whereas the interior modes never violate Bell's inequality. The Hayward regularity parameter ggg affects the correlations only through the Hawking temperature, whose decrease with increasing ggg enhances the preservation of quantum information. These results suggest a close connection between singularity resolution and the robustness of fermionic quantum correlations in regular black-hole spacetimes.
Abstract We transfer the scenario of quantum network nonlocal correlation to the vicinity of a black hole’s event horizon, aiming to evaluate the impact of Hawking effect on network nonlocality within this specific context. In an entanglement swapping network with two bipartite resources and three parties, we examine two scenarios with distinct Hawking radiation locations: one where it affects the endpoint parties’ system and another where it impacts all parties’ system. In both cases, network nonlocality decays due to Hawking radiation and disappears entirely when the Hawking temperature reaches a critical threshold. However, we observe a striking phenomenon: when resource states are maximally entangled and the affected system belongs to the endpoint participants, network nonlocality diminishes but does not vanish throughout the radiation process. Subsequently, we extend our investigation to star and chain networks to evaluate how resource quantity and distribution influence network nonlocality under Hawking radiation. Our results indicate that star networks exhibit greater resilience against Hawking radiation in maintaining nonlocality.