Abstract We investigate the hierarchy of nonlocal correlations for Dirac fields in the Schwarzschild de Sitter (SdS) spacetime. We find that the hierarchical relationship between the nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality remains in the multi-event horizon curved spacetime. It is demonstrated that the NAQC and Bell nonlocality provide a more rigorous characterization of physically inaccessible quantum properties than coherence, as classical information cannot be transmitted across the thermally opaque membrane. Furthermore, when considering an effective equilibrium temperature, an enhancement in quantum nonlocality with increasing temperature is observed, which challenges the conventional understanding that the Hawking effect solely diminishes quantum nonlocality. This study contributes to integrating quantum resource theory within the context of multi-event horizon black holes.
Abstract We investigate the hierarchy of nonlocal correlations for Dirac fields in the Schwarzschild de Sitter (SdS) spacetime. We find that the hierarchical relationship between the nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality remains in the multi-event horizon curved spacetime. It is demonstrated that the NAQC and Bell nonlocality provide a more rigorous characterization of physically inaccessible quantum properties than coherence, as classical information cannot be transmitted across the thermally opaque membrane. Furthermore, when considering an effective equilibrium temperature, an enhancement in quantum nonlocality with increasing temperature is observed, which challenges the conventional understanding that the Hawking effect solely diminishes quantum nonlocality. This study contributes to integrating quantum resource theory within the context of multi-event horizon black holes.
The investigation of nonclassical correlations in curved spacetimes offers key insights into the intersection of quantum information theory and gravitational physics. This paper studies two nonlocal correlation measures, non local advantage of quantum coherence (NAQC) and Bell nonlocality (BN) in a d-dimensional spherically symmetric Einstein-Gauss-Bonnet (EGB) black hole spacetime. We consider two observers (Alice and Rob) initially sharing a maximally entangled Bell state: Alice freely falls into the black hole (inertial Kruskal frame), while Rob accelerates outside the horizon (non-inertial Schwarzschild-like frame). The Unruh-Hawking effect modifies Rob's field modes, requiring Bogoliubov transformations to relate the two frames. We derive the mixed bipartite density matrix for fermionic fields and analytical expressions for NAQC and BN, which depend on Hawking temperature (itself governed by α, d, and rh). Our results show both correlations degrade monotonically with increasing Hawking temperature, confirm the NAQC-BN hierarchical relationship persists in EGB spacetime, and highlighting the impact of high curvature corrections on quantum resources.
Abstract The investigation of nonclassical correlations in curved spacetimes offers key insights into the intersection of quantum information theory and gravitational physics. This paper studies two nonlocal correlation measures, non local advantage of quantum coherence (NAQC) and Bell nonlocality (BN) in a d -dimensional spherically symmetric Einstein–Gauss–Bonnet (EGB) black hole spacetime. We consider two observers (Alice and Rob) initially sharing a maximally entangled Bell state: Alice freely falls into the black hole (inertial Kruskal frame), while Rob accelerates outside the horizon (non-inertial Schwarzschild-like frame). The Unruh–Hawking effect modifies Rob’s field modes, requiring Bogoliubov transformations to relate the two frames. We derive the mixed bipartite density matrix for fermionic fields and analytical expressions for NAQC and BN, which depend on Hawking temperature (itself governed by α α , d , and rh r h ). Our results show both correlations degrade monotonically with increasing Hawking temperature, confirm the NAQC-BN hierarchical relationship persists in EGB spacetime, and highlight higher-curvature corrections’ impact on quantum resources.
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.
Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of the Hawking effect on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, it is significantly affected by Hawking radiation, exhibiting a pronounced difference between physically accessible and inaccessible regions. It is suppressed in the physically accessible region with increasing Hawking temperature and may vanish, while remaining absent in the physically inaccessible region across the parameter regime. For assisted imaginarity distillation, the Hawking effect modifies the assisted fidelity in a state-dependent manner. In the physically accessible region, the fidelity generally decreases with increasing temperature, indicating reduced distillation capability, whereas the physically inaccessible region exhibits the opposite monotonic trend, indicating enhanced distillation capability. These results highlight distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in curved spacetime.
The effect of Hawking radiation on nonlocal advantage of quantum coherence (NAQC) is investigated by considering the Hartle-Hawking temperature under the Schwarzschild space-time. We analyze the characteristics of NAQC in the physically accessible and inaccessible regions. It is found that the minimum value for NAQC is indeed corresponding to the peak of Hawking radiation in accessible regions. Owing to the Hawking effect, quantum resource for the accessible and inaccessible regions is redistributed, and the trade-off relation for the information flow is revealed in the black hole. Besides, we examined the influences of Hawking radius, the distance from the black hole center to particle and the Hartle-Hawking constant on NAQC. It indicates that the smaller Hartle-Hawking constant and larger Hawking radius leads to an increase of NAQC in the physically accessible system. In addition, the hierarchical relationship among various quantum resources is verified in the black hole. If NAQC is achieved in the accessible region, the systemic state must be entangled, steerable and Bell nonlocal. Our findings show that the signatures of quantum atmosphere can be detected via NAQC and it offers a valuable insight on understanding the origination of Hawking radiation.
Abstract We investigate quantum steering of Dirac field for different types of Bell states in Schwarzschild–de Sitter (SdS) spacetime that has a black hole event horizon (BEH) and a cosmological event horizon (CEH). We find that fermionic steerability from Bob to Alice is greater than fermionic steerability from Alice to Bob, while bosonic steerability exhibits the opposite behavior in SdS spacetime. These different properties between fermionic and bosonic steering arise from the differences between Fermi–Dirac statistics and Bose–Einstein statistics. We also find that the Hawking effect of the black hole decreases fermionic steerability. However, the Hawking effect of the expanding universe can enhance fermionic steerability, which differs from the properties of quantum steering in single-event horizon spacetime. Interestingly, we can indirectly protect quantum steering by using appropriate types of Bell states in multi-event horizon spacetime. These conclusions are helpful to guide the task of processing relativistic quantum information for quantum steering in SdS spacetime.