Testing quantum theory on curved space-time with quantum networks and proper time interference

Gravitational time dilation is well tested with atomics clocks. The remarkable precision allows for the verification of this general relativistic effect at mm-scales. However, in all experiments to date the proper time is a classical parameter along classical world-lines of the clocks. Here I will discuss superpositions of proper time and how they affect matter-wave systems in novel ways. I will then extend the analysis to entangled states and show how an experiment with entangled clocks can verify proper time superpositions. This opens the possibility to probe quantum theory on curved space-time for the first time in near future experiments.