Gaussian versus non-Gaussian filtering of phase-insensitive nonclassicality

TL;DR

This paper compares Gaussian and non-Gaussian phase-space filtering methods for detecting nonclassical light, demonstrating that non-Gaussian filtering reveals nonclassicality even at low detection efficiencies through experimental balanced homodyne measurements.

Contribution

It introduces a direct sampling method for non-Gaussian phase-space functions from homodyne data, overcoming previous phase-averaging limitations, and experimentally compares filtering techniques for quantum state analysis.

Findings

Non-Gaussian filtered quasiprobabilities reveal nonclassicality at low efficiencies.

Gaussian $s$-parametrized quasiprobabilities become non-negative below 0.5 efficiency.

Experimental demonstration with heralded single- and two-photon states.

Abstract

Measures of quantum properties are essential to understanding the fundamental differences between quantum and classical systems as well as quantifying resources for quantum technologies. Here two broad classes of bosonic phase-space functions, which are filtered versions of the Glauber-Sudarshan $P$ function, are compared with regard to their ability to uncover nonclassical effects of light through their negativities. Gaussian filtering of the $P$ function yields the family of $s$-parametrized quasiprobabilities, while more powerful regularized nonclassicality quasiprobabilities are obtained by non-Gaussian filtering. A method is proposed to directly sample such phase-space functions for the restricted case of phase-independent quantum states from balanced homodyne measurements. This overcomes difficulties of previous approaches that manually append uniformly distributed optical phases to the measured quadrature data. We experimentally demonstrate this technique for heralded single- and two-photon states using balanced homodyne detection with varying efficiency. The $s$-parametrized quasiprobabilities, which can be directly sampled, are non-negative for detection efficiencies below 0.5. By contrast, we show that significant negativities of non-Gaussian filtered quasiprobabilities uncover nonclassical effects even for low efficiencies.