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We reveal that quadrature squeezing can result in significantly betterquantum-estimation performance with quantum heterodyne detection (of H. P. Yuenand J. H. Shapiro) as compared to quantum homodyne detection for Gaussianstates, which touches an important aspect in the foundational understanding ofthese two schemes. Taking single-mode Gaussian states as examples, we showanalytically that the competition between the errors incurred during tomogramprocessing in homodyne detection and the Arthurs-Kelly uncertainties arisingfrom simultaneous incompatible quadrature measurements in heterodyne detectioncan often lead to the latter giving more accurate estimates. This observationis also partly a manifestation of a fundamental relationship between therespective data uncertainties for the two schemes. In this sense, quadraturesqueezing can be used to overcome intrinsic quantum-measurement uncertaintiesin heterodyne detection.

Surmounting intrinsic quantum-measurement uncertainties in Gaussian-state tomography with quadrature squeezing