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arXiv:2403.11476 · The European Physical Journal C

Genuine N-partite entanglement in Schwarzschild-de Sitter black hole spacetime

Shu-Min Wu, Xiao-Wei Teng, Xiao-Li Huang, Jianbo Lu

Published Nov 27, 2024• 3 citations
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Abstract

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 ( $$n+m=N$$ 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.

DOI
10.1140/epjc/s10052-024-13602-y

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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.
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.
The genuine entanglement of Dirac fields for an N-partite system is investigated in Schwarzschild spacetime and the analysis is carried out using the single-mode approximation. Due to the Hawking effect, quantum entanglement is divided into two parts physically accessible and inaccessible entanglement. We obtain a general analytic expression of genuine N-partite entanglement that includes all accessible and inaccessible entanglement in a Schwarzschild black hole. Unlike bosonic entanglement, the accessible N-partite entanglement of Dirac fields monotonically decreases to a nonzero value with the Hawking temperature. Interestingly, the inaccessible N-partite entanglement is a monotonic or non-monotonic function of the Hawking temperature, depending on the ratio between accessible and inaccessible modes, in contrast to bipartite or tripartite entanglement that is only a monotonic function of the Hawking temperature. Finally, we obtain two restrictive relationships for the quantum information of the black hole. This conclusion provides a new understanding of Hawking effect of the black hole.
Abstract The quantum Bell nonlocality plays a crucial role in quantum information processing. In this paper, we first obtain the quantitative analytical expression of the genuine four-partite Bell nonlocality of any 4-qubit quantum state. Then, we investigate and derive the genuine four-partite nonlocalities in the background of the Schwarzschild black hole and the Schwarzschild–de Sitter spacetime. In the Schwarzschild black hole, it is shown that the Hawking effect destroys the accessible genuine four-partite nonlocality whif the Hawking effect of the Schwarzschild–de Sitter spacetime on the genuine four-partite nonlocality of massless Dirac fields.
Abstract With the complexity of information tasks, the bipartite and tripartite entanglement can no longer meet our needs, and we need more entangled particles to process relativistic quantum information. In this paper, we study the genuine N-partite entanglement and distributed relationships for Dirac fields in the background of dilaton black holes. We present the general analytical expression including all physically accessible and inaccessible entanglement in curved spacetime. We find that the accessible N-partite entanglement exhibits irreversible decoherence as the increase of black hole’s dilaton, and on the other hand the inaccessible N-partite entanglement increases from zero monotonically or non-monotonically, depending on the relative numbers of the accessible to the inaccessible modes, which forms a sharp contrast with the cases of bipartite and tripartite entanglement where the inaccessible entanglement increase only monotonically. We also find two distributed relationships between accessible and inaccessible N-partite entanglement in curved spacetime. The results give us a new understanding of the Hawking radiation.
Abstract It is commonly expected that maximally multipartite entangled states provide the richest quantum correlations and thus represent optimal quantum resources in the Schwarzschild black hole background. Here, by analyzing the genuine N-partite entanglement of fermionic modes near the event horizon, quantified via concurrence, we identify a counterintuitive phenomenon: in this curved spacetime, the genuine multipartite entanglement of a maximally entangled state can be lower than that of a suitably chosen non-maximally entangled state. This observation implies that, from the perspective of quantum resource efficiency, non-maximally entangled multipartite states may outperform their maximal counterparts for quantum information tasks under gravitational effects. Therefore, preparing appropriately engineered non-maximally entangled multipartite states as initial resources provides a more practical and effective approach to quantum information processing in Schwarzschild spacetime.
We investigate genuine multipartite entanglement and genuine tripartite nonlocality of a noisy generalized GHZ state in Schwarzschild-de Sitter spacetime. The genuine multipartite concurrence and optimized Svetlichny parameter are employed to characterize these two quantum correlations. It is shown that the black hole and cosmological event horizons redistribute genuine multipartite entanglement differently among the physically accessible and inaccessible reduced states, while Svetlichny violation occurs only in the physically accessible state. We find that genuine multipartite entanglement can survive in the physically inaccessible states even when genuine tripartite nonlocality is absent. In addition, initial white noise suppresses both correlations, with Svetlichny nonlocality surviving over a narrower parameter region. Furthermore, in the Nariai limit, under the normalization adopted here, the correlations become concentrated in the physically accessible state. These results demonstrate the different robustness of genuine multipartite entanglement and genuine tripartite nonlocality under horizon effects and initial noise.