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arXiv:2503.23302 · The European Physical Journal C

Genuine four-partite Bell nonlocality in the curved spacetime

Guang-Wei Mi, Xiaofen Huang, Shao-Ming Fei, Ting-Gui Zhang

Published Mar 28, 2025• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1140/epjc/s10052-025-14076-2

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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.
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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.
Abstract We study the genuine tripartite nonlocality (GTN) and the genuine tripartite entanglement (GTE) of Dirac fields in the background of a Schwarzschild black hole. We find that the Hawking radiation degrades both the physically accessible GTN and the physically accessible GTE. The former suffers from “sudden death” at some critical Hawking temperature, and the latter approaches to the nonzero asymptotic value in the limit of infinite Hawking temperature. We also find that the Hawking effect cannot generate the physically inaccessible GTN, but can generate the physically inaccessible GTE for fermion fields in curved spacetime. These results show that on the one hand the GTN cannot pass through the event horizon of black hole, but the GTE do can, and on the other hand the surviving physically accessible GTE and the generated physically inaccessible GTE for fermions in curved spacetime are all not nonlocal. Some monogamy relations between the physically accessible GTE and the physically inaccessible GTE are found.
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 We investigate the hierarchy of nonlocal correlations for Dirac fields in the Schwarzschild de Sitter (SdS) spacetime. We find that the hierarchical relationship between the nonlocal advantage of quantum coherence (NAQC) and Bell nonlocality remains in the multi-event horizon curved spacetime. It is demonstrated that the NAQC and Bell nonlocality provide a more rigorous characterization of physically inaccessible quantum properties than coherence, as classical information cannot be transmitted across the thermally opaque membrane. Furthermore, when considering an effective equilibrium temperature, an enhancement in quantum nonlocality with increasing temperature is observed, which challenges the conventional understanding that the Hawking effect solely diminishes quantum nonlocality. This study contributes to integrating quantum resource theory within the context of multi-event horizon black holes.
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.