The Unruh effect in quantum information beyond the single-mode approximation

TL;DR

This paper investigates the limitations of the single-mode approximation in relativistic quantum information, revealing its inaccuracy for general states and identifying conditions where it holds, thus refining entanglement analysis in non-inertial frames.

Contribution

It demonstrates the inaccuracy of the single-mode approximation for arbitrary states and identifies specific wave packets where the approximation is valid, extending previous analyses.

Findings

Single-mode approximation is invalid for most states.

Corrections to previous entanglement studies are provided.

Certain wave packets justify the approximation under specific conditions.

Abstract

We address the validity of the single-mode approximation that is commonly invoked in the analysis of entanglement in non-inertial frames and in other relativistic quantum information scenarios. We show that the single-mode approximation is not valid for arbitrary states, finding corrections to previous studies beyond such approximation in the bosonic and fermionic cases. We also exhibit a class of wave packets for which the single-mode approximation is justified subject to the peaking constraints set by an appropriate Fourier transform.