Estimation of covariance matrix of macroscopic quantum states

TL;DR

This paper introduces a method to estimate the covariance matrix of macroscopic quantum states of light using interference with a classical noisy reference, eliminating the need for a high-intensity local oscillator.

Contribution

It presents a novel detection technique that enables covariance matrix estimation without direct access to position or momentum, suitable for bright squeezed states.

Findings

Allows covariance matrix estimation with Stokes-like detectors

Eliminates need for a high-intensity local oscillator

Applicable to bright squeezed states of light

Abstract

For systems analogous to a linear harmonic oscillator, the simplest way to characterize the state is by a covariance matrix containing the symmetrically-ordered moments of operators analogous to position and momentum. We show that using Stokes-like detectors without direct access to either position or momentum, the estimation of the covariance matrix of a macroscopic signal is still possible using interference with a classical noisy and low-intensity reference. Such a detection technique will allow to estimate macroscopic quantum states of electromagnetic radiation without a coherent high-intensity local oscillator. It can be directly applied to estimate the covariance matrix of macroscopically bright squeezed states of light.