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Precise reconstruction of unknown quantum states from measurement data, aprocess commonly called quantum state tomography, is a crucial component in thedevelopment of quantum information processing technologies. Many differenttomography methods have been proposed over the years. Maximum likelihoodestimation is a prominent example, being the most popular method for a longperiod of time. Recently, more advanced neural network methods have started toemerge. Here, we go back to basics and present a method for continuous variablestate reconstruction that is both conceptually and practically simple, based onconvex optimization. Convex optimization has been used for process tomographyand qubit state tomography, but seems to have been overlooked for continuousvariable quantum state tomography. We demonstrate high-fidelity reconstructionof an underlying state from data corrupted by thermal noise and imperfectdetection, for both homodyne and heterodyne measurements. A major advantageover other methods is that convex optimization algorithms are guaranteed toconverge to the optimal solution.

Simple, reliable and noise-resilient continuous-variable quantum state tomography with convex optimization