  Gravitational redshift is discussed in the context of quantum photons
propagating in curved spacetime. A brief introduction to modelling realistic
photons is first presented and the effect of gravity on the spectrum computed
for photons largely confined along the direction of propagation. It is then
shown that redshift-induced transformations on photon operators with sharp
momenta are not unitary, while a unitary transformation can be constructed for
realistic photons with finite bandwidth. The unitary transformation obtained is
then characterized as a multimode mixing operation, which is a generalized
rotation of the Hilbert-space basis. Finally, applications of these results are
discussed with focus on performance of quantum communication protocols,
exploitation of the effects for quantum metrology and sensing, as well as
potential for tests of fundamental science.
