An effective method to estimate multidimensional Gaussian states

TL;DR

This paper introduces a simple, efficient method for characterizing multidimensional Gaussian states using homodyne detection, offering more stable reconstructions and a tool for detecting non-Gaussian features in optical signals.

Contribution

The paper presents a novel tomography-like scheme for Gaussian states that is more stable and reliable than standard methods, with experimental validation.

Findings

Provides a stable and reliable reconstruction method for Gaussian states

Demonstrates experimental implementation of the scheme

Offers a tool to detect non-Gaussian features in optical signals

Abstract

A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix playing the role of the density matrix and homodyne detection providing Stern-Gerlach-like projections. The major difference stems from a different character of relevant noises: while the statistics of Stern-Gerlach-like measurements is governed by binomial statistics, the detection of quadrature variances correspond to chi-square statistics. For Gaussian and near Gaussian states the suggested method provides, compared to standard tomography techniques, more stable and reliable reconstructions. In addition, by putting together reconstruction methods for Gaussian and arbitrary states, we obtain a tool to detect the non-Gaussian character of optical signals.