  We investigate the interplay between gravity and the quantum coherence
present in the state of a pulse of light propagating in curved spacetime. We
first introduce an operational way to distinguish between the overall shift in
the pulse wavepacket and its genuine deformation after propagation. We then
apply our technique to quantum states of photons that are coherent in the
frequency degree of freedom, as well as to states of completely incoherent
light. We focus on Gaussian profiles and frequency combs and find that the
quantum coherence initially present can enhance the deformation induced by
propagation in a curved background. These results further supports the claim
that genuine quantum features, such as quantum coherence, can be used to probe
the gravitational properties of physical systems. We specialize our techniques
to Earth-to-satellite communication setups, where the effects of gravity are
weak but can be tested with current satellite technologies.
