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 $N$-qubit multipartite system, ${|\mathrm{\Psi }⟩}_{123\dots N}={(\beta {|0⟩}^{\otimes N}+\sqrt{1-{\beta }^2}{|1⟩}^{\otimes N})}_{123\dots N}$, and draw a conclusion that when the black hole approximates to evaporate completely the mutual information of this system will be close to $(N-1)/N$ 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.

• Received 3 November 2013

DOI:https://doi.org/10.1103/PhysRevD.89.065022