Unveiling quantum entanglement degradation near a Schwarzschild black hole

TL;DR

This paper investigates how quantum entanglement between two particles is affected by the presence of a Schwarzschild black hole, revealing that entanglement degrades near the event horizon but remains unaffected far away, with implications for quantum information in curved spacetime.

Contribution

It provides a detailed analysis of entanglement degradation near a black hole without relying on the single mode approximation, highlighting the universality of the phenomenon across different black hole masses.

Findings

Entanglement degrades significantly near the event horizon.

Far from the black hole, entanglement remains largely intact.

The degradation phenomenon is universal across black hole masses.

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.