Gravitational redshift induces quantum interference

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.