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Quantum Information Processing

N-partite coherence of bosonic fields in the background of a Schwarzschild black hole

Shu-Min Wu, Wen-Mei Li, Hao‐Sheng Zeng, X. L. Huang

Published Oct 29, 2022• 5 citations
Publisher
DOI
10.1007/s11128-022-03710-7

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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.
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.