Full statistics of homodyne correlation measurements

TL;DR

This paper derives the complete statistical description of homodyne correlation measurements at high intensities, enhancing the understanding of measurement outcomes and enabling nonclassical light certification.

Contribution

It provides the full statistical framework for homodyne correlation measurements, extending previous analyses to include higher-order statistics and nonclassical light verification.

Findings

Derived the full statistics for homodyne correlation measurements.

Extended analysis to include nonclassical light certification.

Applied framework to coherent, Gaussian, and Fock states.

Abstract

We derive the full statistics of the product events in homodyne correlation measurements, involving a single mode signal, a local oscillator, a linear optical network, and two linear photodetectors. This is performed for the regime of high intensities impinging on the detectors. Our description incorporates earlier proposed homodyne correlation measurement schemes, such as the homodyne cross-correlation and homodyne intensity-correlation measurements. This analysis extends the amount of information retrieved from such types of measurements, since previously attention was paid only to the expectation value of the correlation statistics. As an example, we consider the correlation statistics of coherent, Gaussian, and Fock states. Moreover, nonclassical light is certified on the basis of the variance of the measurement outcome.