Semiparametric estimation of the Hong-Ou-Mandel profile

We apply the theory of semiparametric estimation to a Hong-Ou-Mandel interference experiment with a spectrally entangled two-photon state generated by spontaneous parametric down-conversion. Thanks to the semiparametric approach, we can evaluate the Cramer-Rao bound and find an optimal estimator for a particular parameter of interest without assuming perfect knowledge of the two-photon wave function, formally treated as an infinity of nuisance parameters. In particular, we focus on the estimation of the Hermite-Gauss components of the marginal symmetrized wave function, whose Fourier transform governs the shape of the temporal coincidence profile. We show that negativity of these components is an entanglement witness of the two-photon state.

Automated summary

In this study, we apply the theory of semiparametric estimation to assess the parameters of interest in a Hong-Ou-Mandel interference experiment involving a spectrally entangled two-photon state. Specifically, we focus on estimating the Hermite-Gauss components of the marginal symmetrized wave function, which are shown to serve as an entanglement witness for the two-photon state.