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The European Physical Journal C

Genuine entanglement near multi-event horizon in N-partite system

X. L. Huang, Si-Yu Liu

Published Apr 14, 2025• 1 citation
Publisher

Abstract

Abstract We study genuine N-partite entanglement of massless Dirac fields new a black hole event horizon (BEH) and a cosmological event horizon (CEH) in the Schwarzschild–de Sitter (SdS) spacetime, respectively. We obtain the general analytical expression of genuine N-partite entanglement shared by N observers, each located near the BEH and CEH, respectively. It is shown that genuine N-partite entanglement situated near the BEH can decrease to zero with the decrease of the mass of the black hole, suggesting that the Hawking effect of the black hole destroys quantum entanglement. Because the Hawking effect of the black hole located near the CEH is very weak, its impact on quantum entanglement is negligible. In addition, choosing appropriate initial parameters is beneficial to protecting quantum entanglement in multi-event horizon spacetime.

DOI
10.1140/epjc/s10052-025-14122-z

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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.
Abstract We study Gaussian quantum steering in the Schwarzschild–de Sitter (SdS) spacetime that is endowed with both a black hole event horizon (BEH) and a cosmological event horizon (CEH), giving rise to two different Hawking temperatures. It is shown that the Hawking effect of the black hole always reduces the quantum steering, but the Hawking effect of the expanding universe does not always play the same role. For the first time, we find that the Hawking effect can improve quantum steering. We also find that the observer who locates in the BEH has stronger steerability than the observer who locates in CEH. Further, we study the steering asymmetry, and the conditions for two-way, one-way and no-way steering in the SdS spacetime. Finally, we study the Gaussian quantum steering in the scenario of effective equilibrium temperature. We show that quantum steering reduces monotonically with the effective temperature but now increases monotonically with the Hawking temperature of the black hole, which banishes the belief that the Hawking effect can only destroy quantum steering.