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arXiv:2402.12308 · Classical and Quantum Gravity

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

Samira Elghaayda, Xiang Zhou, Mostafa Mansour

Published Aug 19, 2024• 14 citations
arXivHTMLPDF

Abstract

Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.

DOI
10.1088/1361-6382/ad70ea

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Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.
The influence of Hawking radiation on quantum entanglement for bimodal Gaussian states near a Schwarzschild black hole is investigated. It is shown that for a thermal squeezed state of a bimodal bosonic system the Hawking radiation reduces and even can destroy the entanglement between the mode of a Kruskal observer Alice and the mode of Bob, who is an accelerated observer hovering outside the event horizon of black hole. By contrary, the Hawking radiation increases and even can generate quantum entanglement between Bob and anti-Bob, who is a hypothetical observer inside event horizon. We show that in both these scenarios the competition between the contrary influences produced by Hawking temperature, squeezing and field frequency, may favour the preservation of the quantum entanglement. We investigate also the influence of the thermal environment on the behaviour in time of the entanglement between the considered observers and show that the entanglement is destroyed in a finite time for both considered bipartite scenarios of observers Alice and Bob, and respectively Bob and anti-Bob, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. For a zero temperature of the thermal bath the initial existing entanglement is decreasing over time, but it keeps for all finite times a non-zero value and the logarithmic negativity tends to zero only in the limit of infinite time.
We explore entanglement harvesting using two Unruh-DeWitt (UDW) detectors linearly coupled to the scalar density of a massless spin-1/21/21/2 field in 1+11+11+1 Schwarzschild spacetime. We consider different vacua, including the Boulware, Hartle-Hawking-Israel (HHI), and Unruh vacua, and investigate various configurations of detector trajectories. We find that the transition rate of the static UDW detector exhibits the expected Planckian behavior in the HHI state, while the Unruh state leads to the Helmholtz free energy density of a fermionic thermal bath. We demonstrate that the near-horizon entanglement properties for static detectors in the HHI state have similar behavior to those in Minkowski vacua for uniformly accelerated detectors in Rindler spacetime. We further consider a different interaction Hamiltonian which breaks local Lorentz symmetry and find that the transition rate of the static detector still exhibits Planckian behavior in the HHI state, while in the Unruh state, it leads to the Helmholtz free energy density of a bosonic or fermionic thermal bath corresponding to the static or conformal 2-bein in interaction, respectively. We observe that the anti-Hawking effect enhances the entanglement between the two detectors while the gravitational redshift and Hawking radiation decrease it. In particular, due to the presence of the anti-Hawking effect, the mutual information and concurrence near the event horizon can be non-zero even for static detectors with static 2-bein, which is in contrast with the case of the scalar field. Conclusions are discussed.
Recent theoretical studies propose that Hawking radiation may not emerge strictly at the event horizon but rather from the spatially extended region surrounding a black hole, commonly referred to as the quantum atmosphere. In this work, we explore how this concept influences nonlocal quantum correlations in a bosonic bipartite system located at a certain distance from a Schwarzschild black hole. By employing the measurement-induced nonlocality (MIN) as a quantifier of quantum correlations, we analyze the response of bosonic fields to the thermal and geometric characteristics associated with the Hartle–Hawking vacuum. Those features are associated with the coordinate-dependent metric components of the Schwarzschild background. In this manner, we extend previous studies that primarily focused on the fermionic systems. Our results reveal that when the quantum atmosphere is taken into account, the behavior of MIN departs from its conventional near-horizon profile. In particular, bosonic nonlocal correlations are found to exhibit a pronounced degradation at a finite radial distance from the event horizon and to ultimately vanish as the scaled distance increases further. To some extent this behavior contrasts with the previously considered fermionic case, indicating that bosonic fields provide a potentially stronger response to the quantum atmosphere.
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.
Abstract It is generally believed that quantum entanglement in the maximally entangled states is greater than quantum entanglement in the non-maximally entangled states under a relativistic setting. In this paper, we study quantum entanglement for four different types of Bell-like states of the fermionic modes near the event horizon of a Schwarzschild black hole. It is interesting to find that quantum entanglement in the maximally entangled states is less than quantum entanglement in the non-maximally entangled states in Schwarzschild spacetime. From the perspective of quantum resources, the non-maximally entangled states may have more advantages in curved spacetime compared to the maximally entangled states. This is obviously different from the conclusions in previous paper. For two types of Bell-like states, quantum entanglement suffers sudden death under the Hawking effect of the black hole, and for the other two types of Bell-like states, quantum entanglement can exist forever regardless of the Hawking temperature. Therefore, we should choose appropriate types of Bell-like states to handle relativistic quantum information tasks.
Abstract We investigate how the Hawking effect reshapes distinct quantum resources of Dirac fields in Schwarzschild spacetime beyond the single-mode approximation. By quantifying quantum entanglement and coherence using the negativity, the l 1 -norm of coherence and the relative entropy of coherence, we observe a significant asymmetry in their response to gravitational effects. While the Hawking effect monotonically degrades entanglement and drives it toward a finite residual value, quantum coherence is instead monotonically amplified with increasing Hawking temperature, revealing the black hole as an effective decohering environment for nonlocal correlations but a coherence-enhancing mechanism for local superposition. Notably, we further find that under the influence of the Hawking effect, the maximally entangled state does not necessarily correspond to the largest initial negativity. In fact, its value may even be smaller than that of certain non-maximally entangled states. Our results demonstrate that gravity acts in a highly nonuniform manner on different facets of quantumness and highlight the necessity of resource-adapted state engineering for relativistic quantum information processing near the event horizon of the black hole.