Full statistics of ideal homodyne detection using real (noisy) local oscillator

TL;DR

This paper demonstrates that the complete statistical analysis of balanced homodyne detection can be achieved experimentally even with noisy local oscillators, enabling accurate characterization of quantum states like Fock states.

Contribution

It introduces a method to access full detection statistics in realistic noisy conditions, validating theoretical predictions for Fock state correlations.

Findings

Full statistics of detector outputs can be experimentally obtained despite laser noise.

Experimental verification of two-detector correlation probabilities for Fock states.

Accurate reconstruction of Fock state statistics from phase-randomized coherent states.

Abstract

We show that the full statistics of the two detectors outputs in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state is experimentally accessible despite the excess noise existing in actual laser sources. This possibility is illustrated using phase randomized coherent states signals from which the statistics of Fock states can accurately be obtained. The experimental verification of the recently predicted [K\"{u}hn and Vogel, Phys. Rev. A, \textbf{98}, 013832 (2018)] two-detector correlation probability for Fock states is presented for states $\vert 1 \rangle$ and $\vert 2 \rangle$.