Unveiling quantum entanglement degradation near a Schwarzschild black hole

Eduardo Martín-Martínez, Luis J. Garay, and Juan León
Phys. Rev. D 82, 064006 – Published 3 September 2010

Abstract

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.

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  • Received 7 June 2010

DOI:https://doi.org/10.1103/PhysRevD.82.064006

© 2010 The American Physical Society

Authors & Affiliations

Eduardo Martín-Martínez1, Luis J. Garay2,3, and Juan León1

  • 1Instituto de Física Fundamental, CSIC, Serrano 113-B, 28006 Madrid, Spain
  • 2Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain
  • 3Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain

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Issue

Vol. 82, Iss. 6 — 15 September 2010

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