Simple, Reliable, and Noise-Resilient Continuous-Variable Quantum State Tomography with Convex Optimization

Journal article, 2022

Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum informa-tion 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 prac-tically 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 and imperfect detection, for both homodyne and heterodyne measurements. A major advan-tage over other methods is that convex optimization algorithms are guaranteed to converge to the optimal solution.