Effect of relativistic acceleration on localized two-mode Gaussian quantum states

TL;DR

This paper analyzes how uniform acceleration affects the quantum states of two localized Gaussian wave packets, revealing complex phenomena like entanglement sudden death and providing a framework for quantum information in relativistic settings.

Contribution

It introduces a generalized Rindler frame and derives a Gaussian channel transformation for arbitrary accelerations and distances, advancing understanding of relativistic quantum information.

Findings

Vacuum entanglement is highly sensitive to spatial separation and acceleration.

The study quantifies fidelity and bounds on capacities of the resulting quantum channels.

New insights into entanglement dynamics under relativistic acceleration.

Abstract

We study how an arbitrary Gaussian state of two localized wave packets, prepared in an inertial frame of reference, is described by a pair of uniformly accelerated observers. We explicitly compute the resulting state for arbitrarily chosen proper accelerations of the observers and independently tuned distance between them. To do so, we introduce a generalized Rindler frame of reference and analytically derive the corresponding state transformation as a Gaussian channel. Our approach provides several new insights into the phenomenon of vacuum entanglement such as the highly non-trivial effect of spatial separation between the observers including sudden death of entanglement. We also calculate the fidelity of the two-mode channel for non-vacuum Gaussian states and obtain bounds on classical and quantum capacities of a single-mode channel. Our framework can be directly applied to any continuous variable quantum information protocol in which the effects of acceleration or gravity cannot be neglected.