Estimation of covariance matrix of macroscopic quantum states

László Ruppert, Vladyslav C. Usenko, Radim Filip

Published 2015-11-20Version 1

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 position and momentum. We show that without direct access to either position or momentum, the estimation of the covariance matrix of non-classical states is still possible using interference with a classical noisy and low- intensity reference and linear detection of energy. 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.