Towards Communication in a Curved Spacetime Geometry

TL;DR

This paper explores how spacetime curvature influences quantum communication signals, deriving explicit formulas for wavefunction distortion due to gravity, with practical implications for space-based quantum networks.

Contribution

It provides a novel explicit expression linking Riemann curvature to wavefunction distortion and analyzes effects in specific geometries like AdS and Schwarzschild.

Findings

Spacetime curvature causes a 0.10 radian phase shift in Earth-ISS communication.

Quadrupole astigmatism leads to 12.2% mode cross-talk in solar system transmissions.

Gravitational distortions are significant and require correction for reliable quantum communication.

Abstract

The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti-de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10~radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism can cause a 12.2 % cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.