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.
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.
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.
Abstract Nonlocal advantage of quantum coherence (NA-QC) is a relatively robust non-classical correlation and can be achieved by coherence complementary relations. In this work, we investigate NA-QC based on various coherence measures within the theoretical framework of a Garfinkle-Horowitz-Strominger dilation black hole. Interestingly, NA-QC exhibits monotonically decreasing evolutionary features with the growing dilation parameter in the physically accessible regions. Furthermore, the hierarchical relationship among NA-QC, quantum steerability and Bell-nonlocality is analyzed under the influence of Hawking radiation. It is shown that NA-QC is a subset of Bell-nonlocality and quantum steering is a superset of Bell-nonlocality. Additionally, to achieve more quantum resources, we propose a feasible physical scheme to control NA-QC by using optimal parity-time ( P T )-symmetric operations. The amount of NA-QC can be effectively enhanced in the certain time interval for the physical accessible state in the context of black hole. These results might play important roles for understanding quantum information theory under the curved space-time.
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.
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.
We investigate quantum state texture, genuine multipartite entanglement, and tripartite nonlocality of a tripartite mixed state in the black hole quantum atmosphere. By introducing the Hartle-Hawking local temperature into the Bogoliubov coefficients, we characterize the influence of the local Hawking effect on both physically accessible and inaccessible reduced states. We find that the extrema of these three quantities all lie in the same near horizon region and shift outward with increasing local Hawking temperature, coinciding with the peak region of the local Hawking temperature and indicating that different aspects of tripartite quantum information are most sensitive to the local Hawking effect in the same atmospheric region. In contrast to genuine multipartite entanglement, tripartite nonlocality is more fragile and is suppressed under stronger local Hawking effects. These results provide a unified characterization of density matrix restructuring, entanglement redistribution, and nonlocality in tripartite mixed states affected by the black hole quantum atmosphere.
Quantum imaginarity, as a critical resource metric for quantifying intrinsic nonreal coherence encoded in quantum states, exhibits nontrivial evolutionary behaviors in curved spacetime backgrounds. This work focuses on bipartite Dirac field reduced states in the quantum atmosphere of a static Schwarzschild black hole, aiming to explore the modulation of three mainstream imaginarity measures by Hawking thermal radiation. We reveal that the relative-entropy imaginarity, the geometric imaginarity and robustness of imaginarity, the fully accessible state presents a valley-shaped radial profile with a local minimum inside the quantum atmosphere, while the cross-coupling and fully inaccessible states follow opposite peak-shaped trends. Further analysis demonstrates that the Hartle-Hawking constant significantly strengthens the redistribution effect of imaginarity across both regions, whereas an increase in the event horizon radius weakens such redistribution and flattens the extremum features. These findings offer a new perspective for decoding the information structure of black hole quantum atmospheres and the intrinsic quantum nature of Hawking radiation.