Distribution of distance-based quantum resources outside a radiating Schwarzschild black hole

Abstract: We obtain analytical expressions for distance-based quantum resources and examine their distribution in the proximity of a Schwarzschild black hole (SBH) within a curved background. For an observer in free fall and their stationary counterpart sharing the Gisin state, the quantum resources are degraded at an infinite Hawking temperature. The extent of this degradation that occurs as the SBH evaporates is contingent upon the fermionic frequency mode, Gisin state parameters, and the distance between the observer and the event horizon (EH). In the case of two accelerating detectors in Minkowski spacetime interacting with quantum fluctuating scalar fields (QFSF), we find that quantum coherence and discord exhibit sudden disappearance for certain initial states and sudden reappearance for others except entanglement, regardless of the Unruh temperature. We also discover that the quantum resources of one detector can be transferred to another in the case of two stationary detectors through a fluctuating quantum field outside the SBH. We demonstrate that, in contrast to coherence and discord, we are unable to regenerate entanglement for a given initial state and that they are equal for different vacuum states. In certain circumstances, the presence of EHs does not significantly reduce the available resources, as it turns out that all interesting phenomena occur within EHs. Since the world is basically non-inertial, it is necessary to understand the distribution of quantum resources within a relativistic framework.