  Quantum technologies present new opportunities for fundamental tests of
nature. One potential application is to probe the interplay between quantum
physics and general relativity - a field of physics with no empirical evidence
yet. Here we show that quantum networks open a new window to test this
interface. We demonstrate how photon mediated entanglement between atomic or
atom-like systems can be used to probe time-dilation induced entanglement and
interference modulation. Key are non-local measurements between clocks in a
gravitational field, which can be achieved either through direct photon
interference or by using auxiliary entanglement. The resulting observable
depends on the interference between different proper times, and can only be
explained if both quantum theory and general relativity are taken into account.
The proposed protocol enables clock interferometry on km-scale separations and
beyond. Our work thus shows a realistic experimental route for a first test of
quantum theory on curved space-time, opening up new scientific opportunities
for quantum networks.
