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arXiv:2412.02927 · Annalen der Physik

Impact of the Hawking Effect on the Fully Entangled Fraction of Three‐Qubit States in Schwarzschild Spacetime

Guang‐Wei Mi, Xiaofen Huang, Shao‐Ming Fei, Tinggui Zhang

Published Nov 30, 2024• 9 citations
arXivHTMLPDF

Abstract

Abstract Wu et al. [J. High Energ. Phys. 2023 , 232 (2023)] first found that the fidelity of quantum teleportation with a bipartite entangled resource state, completely determined by the fully entangled fraction (FEF) characterized by the maximal fidelity between the given quantum state and the set of maximally entangled states, can monotonically increase in Schwarzschild spacetime. The Hawking effect on the FEF of quantum states in tripartite systems is investigated. In this study, it is showed that the Hawking effect of a black hole may both decrease and increase the FEF in Schwarzschild spacetime. For an initial X‐type state, it is found that the Hawking effect of the black hole has both positive and negative impacts on the FEF of Dirac fields, depending on the selection of initial states. For an initial W‐like state, the Hawking effect of the black hole has only a positive impact on the FEF of Dirac fields, independent of the selection of initial states. These results provide an insightful view of quantum teleportation in multipartite systems under the influence of Hawking effects, from the perspective of quantum information and general relativity.

DOI
10.1002/andp.202400308

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Abstract Wu et al. [J. High Energ. Phys. 2023 , 232 (2023)] first found that the fidelity of quantum teleportation with a bipartite entangled resource state, completely determined by the fully entangled fraction (FEF) characterized by the maximal fidelity between the given quantum state and the set of maximally entangled states, can monotonically increase in Schwarzschild spacetime. The Hawking effect on the FEF of quantum states in tripartite systems is investigated. In this study, it is showed that the Hawking effect of a black hole may both decrease and increase the FEF in Schwarzschild spacetime. For an initial X‐type state, it is found that the Hawking effect of the black hole has both positive and negative impacts on the FEF of Dirac fields, depending on the selection of initial states. For an initial W‐like state, the Hawking effect of the black hole has only a positive impact on the FEF of Dirac fields, independent of the selection of initial states. These results provide an insightful view of quantum teleportation in multipartite systems under the influence of Hawking effects, from the perspective of quantum information and general relativity.
A bstract Previous studies have shown that the Hawking effect always destroys quantum correlations and the fidelity of quantum teleportation in the Schwarzschild black hole. Here, we investigate the fidelity of quantum teleportation of Dirac fields between users in Schwarzschild spacetime. We find that, with the increase of the Hawking temperature, the fidelity of quantum teleportation can monotonically increase, monotonically decrease, or non-monotonically increase, depending on the choice of the initial state, which means that the Hawking effect can create net fidelity of quantum teleportation. This striking result banishes the extended belief that the Hawking effect of the black hole can only destroy the fidelity of quantum teleportation. We also find that quantum steering cannot fully guarantee the fidelity of quantum teleportation in Schwarzschild spacetime. This new unexpected source may provide a new idea for the experimental evidence of the Hawking effect.
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.
Abstract We investigate the robustness of quantum teleportation in the presence of strong gravitational fields by analyzing bipartite mixed states derived from tripartite GHZ and W -class states near black hole event horizons. Considering a scenario where two observers approach the horizon of either a Schwarzschild or a Garfinkle–Horowitz–Strominger Dilaton black hole while a third remains in flat space, we quantify the teleportation fidelity of the resulting bipartite channels after tracing out one party. Through the quantization of Dirac fields and Bogoliubov transformations, we compute the teleportation fidelity under the influence of Hawking radiation and spacetime curvature. Our results show that while entanglement degrades, teleportation fidelity remains above the classical threshold of f > 2 3 for channels derived from W -class states, but not for GHZ -derived states. This indicates that quantum teleportation can remain feasible near black holes provided the initial entangled state retains useful bipartite entanglement.
Abstract Complex quantum information tasks in a gravitational background require multipartite entanglement for effective processing. Therefore, it is necessary to investigate the properties of multipartite entanglement in a relativistic setting. In this paper, we study genuine N-partite entanglement of massless Dirac fields in the Schwarzschild-de Sitter (SdS) spacetime, characterized by the presence of a black hole event horizon (BEH) and a cosmological event horizon (CEH). We obtain the general analytical expression of genuine N-partite entanglement shared by n observers near BEH and m ( n+m=Nn+m=Nn+m=N n + m = N ) observers near CEH. It is shown that genuine N-partite entanglement monotonically decreases with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. It is interesting to note that genuine N-partite entanglement is a non-monotonic function of the cosmological constant, meaning that the Hawking effect of the expanding universe can enhance quantum entanglement. This result contrasts with multipartite entanglement in single-event horizon spacetime, offering a new perspective on the Hawking effect in multi-event horizon spacetime.
Gravitational effects associated with black holes are widely believed to universally degrade quantum entanglement, with the loss of maximal entanglement being particularly severe and even irreversible for bosonic fields. In this work, we investigate the entanglement properties of the four-qubit cluster state (CL4CL_4CL4​) for fermionic fields in the curved spacetime of a Schwarzschild black hole. Remarkably, we uncover a counterintuitive phenomenon: as the Hawking temperature increases, quantum entanglement (111-333 tangle) of the CL4CL_4CL4​ state remains strictly constant, indicating a ``complete freezing of initially maximal entanglement". This constitutes the first explicit example in which maximal entanglement remains perfectly preserved in a black hole environment, defying the conventional expectation that gravitational effects can only suppress maximal quantum correlations. Moreover, our results indicate that, within a relativistic framework, the CL4CL_4CL4​ state constitutes a high-quality quantum resource with potential applications in relativistic quantum information processing, and may significantly improve the performance of such protocols.
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.