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arXiv:2310.15675 · The European Physical Journal C

Quantumness near a Schwarzschild black hole

Saeed Haddadi, Mikhail A. Yurischev, Mahmoud Youssef Abd‐Rabbou, Majid Azizi, Mohammad Reza Pourkarimi, Mehrdad Ghominejad

Published Jan 17, 2024• 21 citations
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Abstract

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.

DOI
10.1140/epjc/s10052-024-12393-6

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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 quantum characteristics around Schwarzschild black hole, exploring various quantum resources and their interplay in curved space-time. Our analysis reveals intriguing behaviors of quantum coherence, global and genuine multipartite entanglement, first-order coherence, and mutual information in different scenarios. Initially, we consider three particles shared among Alice, Bob, and Charlie in a Minkowski space far from the event horizon, where these particles are correlated via Greenberger-Horne-Zeilinger-type correlation. While Alice's particle remains in Minkowski space, Bob and Charlie accelerate towards the event horizon, experiencing black hole evaporation and generating antiparticles correlated via the Hawking effect. We employ the Kruskal basis formulation to derive a pentapartite pure state shared among particles inside and outside the event horizon. Investigating different scenarios among particles both inside and outside the event horizon, we observe how quantum resources evolve and distribute among consideration of different particles with Hawking temperature and mode frequency. The trade-off relationship between first-order coherence and concurrence fill persists, indicating the intricate interplay between coherence and entanglement. Notably, the mutual information between external observers and particles inside the black hole becomes nonzero, deepening our understanding of quantum effects in curved space-time and shedding light on the quantum nature of the black hole. We believe that these findings will pave the way for future investigations into the fundamental quantum mechanical aspects of gravity under extreme environments.
We consider a stationary quantum system consisting of two non-interacting yet entangled subsystems, ΞΞΞ and ΓΓΓ. We identify a quantum theory characterizing ΞΞΞ such that, in the quantum-to-classical crossover of the composite system, ΓΓΓ behaves as a test particle within the gravitational field of a Schwarzschild Black Hole (SBH) near its event horizon. We then show that this same quantum theory naturally provides a representation of ΞΞΞ in terms of bosonic modes, whose features match those of the Hawking radiation; this facilitates the establishment of precise relations between the phenomenological parameters of the SBH and the microscopic details of the quantum model for ΞΞΞ. Finally, we recognize that the conditions used to characterize ΓΓΓ and ΞΞΞ coincide with those required by the Page and Wootters mechanism for identifying an evolving system and an associated clock. This leads us to discuss how the quantum model for ΞΞΞ endows the SBH with all the characteristics of a "perfect" clock.
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 black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.
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.