Semiparametric estimation in Hong-Ou-Mandel interferometry

TL;DR

This paper applies semiparametric estimation to Hong-Ou-Mandel interferometry with entangled photons, enabling optimal parameter estimation without full knowledge of the quantum state, and identifies entanglement through wavefunction components.

Contribution

It introduces a semiparametric approach to quantum interferometry, allowing for efficient estimation of wavefunction features without complete state knowledge.

Findings

Derived the Cramér-Rao bound for the experiment

Identified entanglement witness via wavefunction components

Developed an optimal estimator for specific parameters

Abstract

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 downconversion. Thanks to the semiparametric approach we can evaluate the Cram\'er-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 symmetrised wavefunction, 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.