In this paper, we compute the various bipartite quantum correlations in the presence of the (4 + n)-dimensional Schwarzschild black hole. In particular, we focus on the n-dependence of various bosonic bipartite entanglements. For the case between Alice and Rob, where the former is free falling observer and the latter is at the near-horizon region, the quantum correlation is degraded compared to the case in the absence of the black hole. The degradation rate increases with decreasing n. We also compute the physically inaccessible correlations. It is found that there is no creation of quantum correlation between Alice and AntiRob. For the case between Rob and AntiRob the quantum entanglement is created although they are separated in the causally disconnected regions. It is found that contrary to the physically accessible correlation the entanglement between Rob and AntiRob decreases with increasing n.
We study entanglement degradation near the horizons of regular, Reissner-Nordström, and Schwarzschild-de Sitter black holes, considering the Bardeen, Hayward, and generalized Hayward metrics as regular black holes. To this end, we compute the entanglement negativity,
N, for two Unruh-like modes of a scalar field shared by Alice, who is inertial, and Rob, who hovers at a fractional offset
ρ outside the horizon of the backgrounds under consideration. For each geometry, we locally approximate the metric by a Rindler patch characterized by Rob's proper acceleration
a0. Because this Rindler approximation breaks down near the extremal limit, we also compute a near-extremal cutoff. Tracing over the inaccessible Rindler wedge yields a mixed Alice-Rob state, from which we evaluate
N as a function of the mode frequency
ω and the acceleration
a0. In all geometries considered, except for one,
N increases monotonically with the parameter distinguishing that geometry form the Schwarzschild one. The exception is the Reissner-Nordström metric, for which
N exhibits a shallow local minimum at a particular value of the charge. We also find that the Reissner-Nordström metric is the only background for which the negativity falls below that of the Schwarzschild case. Among all cases studied, the Schwarzschild-de Sitter spacetime provides the strongest protection of entanglement. Finally, across all backgrounds, high-frequency modes undergo less degradation than low-frequency modes. These results suggest that entanglement may serve as a useful probe for distinguishing Schwarzschild spacetime from other geometries.
Entanglement degradation appears to be a generic prediction in relativistic quantum information whenever horizons restrict access to a region of spacetime. This property has been previously explored in connection with the Unruh effect, where a bipartite entangled system composed of an inertial observer (Alice) and a uniformly accelerated observer (Rob) was studied, with entanglement degradation caused by the relative acceleration---and with equivalent results for the case when Alice is freely falling into a black hole and Rob experiences a constant proper acceleration as a stationary near-horizon observer. In this work, we show that a similar degradation also occurs in the case of an entangled system composed of an inertial observer (Alice) and a ``diamond observer'' (Dave) with a finite lifetime. The condition of a finite lifetime is equivalent to the restriction of Dave's access within a causal diamond. Specifically, if the system starts in a maximally entangled state, prepared from Alice's perspective, entanglement degradation is enforced by the presence of the diamond's causal horizons.
We investigate the Hawking effect on entangled fields. By considering a scalar field which is in a two-mode squeezed state from the point of view of freely falling (Kruskal) observers crossing the horizon of a Schwarzschild black hole, we study the degradation of quantum and classical correlations in the state from the perspective of physical (Schwarzschild) observers confined outside the horizon. Due to monogamy constraints on the entanglement distribution, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the limit of a small-mass black hole, no bipartite entanglement is detected outside the horizon, while the genuine multipartite entanglement interlinking the inner and outer regions grows infinitely.
We quantify the nature of the information loss in a Schwarzschild black hole as a function of its mass. We consider a scalar field in a two-mode squeezed state in the far past, and study the degradation of entanglement and classical correlations from the perspective of observers outside the black hole due to the Hawking radiation. Due to monogamy constraints on the distribution of entanglement, we show that the lost bipartite entanglement is recovered as multipartite entanglement among modes inside and outside the horizon. In the black hole evaporation limit, all bipartite entanglement between modes outside the black hole vanishes while the genuine multipartite entanglement grows infinitely.