When heterodyning beats homodyning: an assessment with quadrature moments

Abstract

We examine the moment-reconstruction performance of both the homodyne and heterodyne (double-homodyne) measurement schemes for arbitrary quantum states and introduce moment estimators that optimize the respective schemes for any given data. In the large-data limit, these estimators are as efficient as the maximum-likelihood estimators. We then illustrate the superiority of the heterodyne measurement for the reconstruction of the first and second moments by analyzing Gaussian states and many other significant non-classical states.

16 pages, 6 figures

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• Towards optimal quantum tomography with unbalanced homodyning
• Estimation of Wigner distribution of single mode Gaussian states: a comparative study
• Characterizing Gaussian quantum processes with Gaussian resources
• Asymmetry effects in homodyne and heterodyne measurements: Positive operator-valued measures and asymptotic security of Gaussian-continuous-variable quantum key distribution
• Joint measurement of complementary observables in moment tomography