Dynamics of Entanglement in Schwarzschild Black Holes

TL;DR

This paper investigates how entanglement, measured by concurrence, evolves near Schwarzschild black holes under Hawking radiation and noise, revealing distinct behaviors of accessible and inaccessible entanglement.

Contribution

It introduces a detailed analysis of concurrence dynamics in black hole environments, including trade-offs and effects of different noise channels, which is novel in quantum gravity studies.

Findings

Physically accessible concurrence decreases with Hawking temperature.

Physically inaccessible concurrence increases monotonically with Hawking temperature.

Sudden death of concurrence occurs in phase flip and bit flip channels, but not in phase damping.

Abstract

To characterize the effect of Hawking radiation induced by the quantum atmosphere beyond the event horizon on entanglement, we employ concurrence as the entanglement measure for a bipartite mixed state and investigate its evolution with Hawking temperature. We find that the physically accessible concurrence decreases as the Hawking acceleration increases, whereas the physically inaccessible concurrence exhibits the opposite behavior, increasing monotonically from zero. We further establish several trade-off relations on concurrence, revealing its distribution between physically accessible and inaccessible regions. Additionally, we study the dynamics of concurrence under three types of channel noise. The results indicate that the evolution of concurrence depends on the specific noise channel: unlike the phase damping channel, sudden death of concurrence occurs in both phase flip and bit flip channels, the concurrence exhibits a certain symmetry with respect to the noise parameter during its evolution under bit flip channel noise.