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.
Highlights
Communication complexity, quantum cryptography and randomness generation [10,11,12,13,14,15]
We study the properties of genuine tripartite nonlocality (GTN) and genuine tripartite entanglement (GTE) of Dirac fields in the background of a Schwarzschild black hole
According to the exchange symmetry for Bob and Charlie, we can get the Svetlichny value and GTE between modes A, CI and CI I, the modes A, BI I and CI I, but cannot generate the physically inaccessible GTN, i.e., entanglement can pass through the event horizon of black hole, and nonlocality cannot
Summary
The combination of quantum information science, relativity theory and quantum field theory gives us a deeper understanding of quantum mechanics. Tripartite entanglement in the relativistic framework was investigated [33,34,35,36,37,38,39]. Note that, in these works, the measure of GTE is based on the concept of logarithmic negativity [40,41], and the measure of GTE based on concurrence [42,43] was not used in Schwarzschild spacetime. Alice is a Kruskal observer who stays stationarily at an asymptotically flat region, while Bob and Charlie are Schwarzschild observers who hover near the event horizon of the black hole. The Hawking effect would make the information tunnelling from the exterior to the interior of the event horizon, such that a correlated
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