Entangled wavepackets in the vacuum

TL;DR

This paper investigates the entanglement properties of localized wavepackets in quantum field theory, revealing how they can be nearly purified by mirror modes and analyzing the relationship between localization and quantum purity.

Contribution

It introduces a method to analyze entangled wavepackets in the vacuum, especially near black hole horizons, and quantifies the localization-purity trade-off.

Findings

Localized wavepackets are nearly purified by mirror modes behind the horizon.

Entanglement entropy of a wavepacket in Minkowski vacuum is calculated.

Purity increases as wavepackets delocalize.

Abstract

Motivated by the black hole firewall problem, we find highly entangled pairs of spatially localized modes in quantum field theory. We demonstrate that appropriately chosen wavepackets localized outside the horizon are nearly purified by 'mirror' modes behind the horizon. In addition, we calculate the entanglement entropy of a single localized wavepacket in the Minkowski vacuum. In all cases we study, the quantum state of the system becomes pure in the limit that the wavepackets delocalize; we quantify the trade-off between localization and purity.