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

Precise reconstruction of unknown quantum states from measurement data has been researched for decades. This process, known as quantum state tomography, is of fundamental interest and nowadays also a crucial component in the development of quantum information processing technologies. Many different tomography methods have been proposed over the years. Maximum likelihood estimation is a prominent example, being the most popular method for a long period of time. Recently, more advanced neural network methods have started to emerge. Here, we go back to basics and present a method for continuous variable state reconstruction that is both conceptually and practically simple, based on convex optimization. Convex optimization has been used for process tomography and qubit state tomography, but seems to have been overlooked for continuous variable quantum state tomography. We demonstrate high-fidelity reconstruction of an underlying state from data corrupted by thermal noise or imperfect detection, for both homodyne and heterodyne measurements. A major advantage over widely used iterative maximum likelihood methods is that convex optimization algorithms are guaranteed to converge to the optimal solution.