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arXiv:quant-ph/0607214 · Journal of the Korean Physical Society

Hawking Effects on the Entanglement near a Schwarzschild Black Hole

Doyeol Doyeol

Published Feb 15, 2007• 7 citations
arXivHTMLPDF

Abstract

Hawking radiation effects on an entangled pair near the event horizon of a Schwarzschild black hole are investigated. The Hawking radiation was found to degrade both the quantum coherence of the entangled state and the mutual correlations of the entangled pair. When the black hole evaporated completely, the measure of entanglement vanished, but the classical correlation between the entangled pair still remained.

DOI
10.3938/jkps.50.368

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Hawking radiation effects on an entangled pair near the event horizon of a Schwarzschild black hole are investigated. The Hawking radiation was found to degrade both the quantum coherence of the entangled state and the mutual correlations of the entangled pair. When the black hole evaporated completely, the measure of entanglement vanished, but the classical correlation between the entangled pair still remained.
In this paper, the effect of Hawking radiation on the multipartite entanglement of Dirac particles in the background of a Schwarzschild black hole is investigated. It is shown that all the 1-tangles decrease as the Hawking temperature grows, and the Coffman--Kundu--Wootters monogamy inequality is always saturated in this system. It is also shown that the entanglement's status of subsystems, which have the same quantum state, depend on its detector's position, and this proposition can be generalized to a multipartite system. Then, we find that the Hawking effect does not change the entanglement structure of the quantum state in Schwarzschild space-time. In addition, we discuss the distributions of quantum information and find that not only is the entanglement redistributed, but also the mutual information is distributed to the physical inaccessible region. At last, we calculate the mutual information of a NNN-qubit multipartite system, ${|\mathrm{\ensuremath{\Psi}}⟩}_{123\dots{}N}={(\ensuremath{\beta}{|0⟩}^{\ensuremath{\bigotimes}N}+\sqrt{1\ensuremath{-}{\ensuremath{\beta}}^{2}}{|1⟩}^{\ensuremath{\bigotimes}N})}_{123\dots{}N}$, and draw a conclusion that when the black hole approximates to evaporate completely the mutual information of this system will be close to $(N\ensuremath{-}1)/N$ of the original if a particle freely falls in toward a Schwarzschild black hole and locates near the event horizon, and the other particles remain in the asymptotically flat region.
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.
We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.
Abstract The merging of quantum information science with the relativity theory presents novel opportunities for understanding the enigmas surrounding the transmission of information in relation to black holes. For this purpose, we study the quantumness near a Schwarzschild black hole in a practical model under decoherence. The scenario we consider in this paper is that a stationary particle in the flat region interacts with its surroundings while another particle experiences free fall in the vicinity of a Schwarzschild black hole’s event horizon. We explore the impacts of Hawking radiation and decoherence on the system under investigation and find that these effects can limit the survival of quantum characteristics, but cannot destroy them completely. Hence, the results of this study possess the potential to yield valuable insights into the comprehension of the quantum properties of a real system operating within a curved space-time framework.
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.
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.