  We use quantum field theory in curved spacetime to show that gravitational
redshift induces a unitary transformation on the quantum state of propagating
photons. This occurs for realistic photons characterized by a finite bandwidth,
while ideal photons with sharp frequencies do not transform unitarily. We find
that the transformation is a mode-mixing operation, and we devise a protocol
that exploits gravity to induce a Hong-Ou-Mandel-like interference effect on
the state of two photons. Testing the results of this work can provide a
demonstration of quantum field theory in curved spacetime.
