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Journal of Physics Conference Series

The cosmological constant effect on the quantum entanglement

A. Mohadi, N. Mebarki, M. Boussahel

Published Jul 1, 2019• 2 citations
Publisher

Abstract

In Schwarzschild-de Sitter space-time, the effect of a gravitational field near a massive body black hole on the spin entanglement has been studied for two-qubits in the case of triplet and singlet states of a two particles system in a circular geodesic motion. It is found that the effect of the cosmological constant on the robustness of the Wooters concurrence is more important in the triplet state than in the singlet one even in the extended region around the black hole

DOI
10.1088/1742-6596/1269/1/012014

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In Schwarzschild-de Sitter space-time, the effect of a gravitational field near a massive body black hole on the spin entanglement has been studied for two-qubits in the case of triplet and singlet states of a two particles system in a circular geodesic motion. It is found that the effect of the cosmological constant on the robustness of the Wooters concurrence is more important in the triplet state than in the singlet one even in the extended region around the black hole
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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.
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.
The effect of a classical gravitational field on the spin entanglement of a system of two spin- particles moving in the curved spacetime is discussed. The system is described by a two-particle Gaussian wave packet represented in the momentum space and both the acceleration of the system and the curvature of the spacetime produce a Wigner rotation acting on the wave packet as it moves along a path in the curved spacetime. By calculating the reduced density operator at a final point, we focus on the spin entanglement of the system. In a spherically symmetric and static gravitational field, for example a charged black hole, there can be particular paths on which the Wigner rotation is trivial and so the initial reduced density matrix remains intact. This causes the spin entanglement to be invariant during the motion. The spin entanglement descends to zero by increasing the angular velocity of the mean centroid of the system as well as increasing the proper time during which the centroid moves on its circular path around the center.
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.
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.