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

TL;DR

This paper demonstrates that quantum metrology using the Hong-Ou-Mandel effect in a gravitational setting can significantly improve the precision of estimating Earth's post-Newtonian parameters, surpassing classical methods.

Contribution

It introduces a quantum metrology approach leveraging the HOM effect to estimate relativistic parameters with unprecedented accuracy.

Findings

Uncertainty in b3 and b2 parameters can reach 10^{-8} to 10^{-12}

Quantum states enhance estimation precision

Method outperforms classical estimation techniques

Abstract

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.