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

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