Unveiling quantum entanglement degradation near a Schwarzschild black hole

© 2010 The American Physical Society. The authors would like to thank Bei-Lok Hu, Ivette Fuentes, Robert Mann, and Paul Alsing for the helpful discussions during the International Workshop on Relativisitc Quantum Information (RQI-N 2010). The authors also thank Jorma Louko and Carlos Barcelo´ for their helpful comments and observations. This work was partially supported by the Spanish MICINN Projects No. FIS2008-05705/FIS and No. FIS2008-06078-C03-03, the CAM research consortium QUITEMAD S2009/ESP- 1594, and the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042). E. M-M. was partially supported by CSIC Grant No. JAE-PREDOC2007 .
We analyze the entanglement degradation provoked by the Hawking effect in a bipartite system Alice-Rob when Rob is in the proximities of a Schwarzschild black hole while Alice is free falling into it. We will obtain the limit in which the tools imported from the Unruh entanglement degradation phenomenon can be used properly, keeping control on the approximation. As a result, we will be able to determine the degree of entanglement as a function of the distance of Rob to the event horizon, the mass of the black hole, and the frequency of Rob's entangled modes. By means of this analysis we will show that all the interesting phenomena occur in the vicinity of the event horizon and that the presence of event horizons do not effectively degrade the entanglement when Rob is far off the black hole. The universality of the phenomenon is presented: There are not fundamental differences for different masses when working in the natural unit system adapted to each black hole. We also discuss some aspects of the localization of Alice and Rob states. All this study is done without using the single mode approximation.
Comunidad de Madrid
Spanish MICINN
Consolider-Ingenio
CSIC
Depto. de Física Teórica
Fac. de Ciencias Físicas
TRUE
pub