Outperforming classical estimation of Post-Newtonian parameters of Earth's gravitational field using quantum metrology

The Hong-Ou-Mandel (HOM) effect is analyzed for photons in a modified Mach-Zehnder setup with two particles experiencing different gravitational potentials, which are later recombined using a beam-splitter. It is found that the HOM effect depends directly on the relativistic time dilation between the arms of the setup. This temporal dilation can be used to estimate the $\gamma$ and $\beta$ parameters of the parameterized post-Newtonian formalism. The uncertainty in the parameters $\gamma$ and $\beta$ are of the order $ 10^{-8}-10^{-12}$, depending on the quantum state employed.