  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.
