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

TL;DR

This paper introduces a simple, reliable, and noise-resilient method for continuous-variable quantum state tomography using convex optimization, offering guaranteed convergence and high-fidelity reconstruction even with noisy data.

Contribution

It presents a novel convex optimization-based approach for continuous-variable quantum state tomography, filling a gap in existing methods and demonstrating robustness against noise.

Findings

High-fidelity state reconstruction from noisy data

Guaranteed convergence of the optimization algorithm

Effective for both homodyne and heterodyne measurements

Abstract

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 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 and imperfect detection, for both homodyne and heterodyne measurements. A major advantage over other methods is that convex optimization algorithms are guaranteed to converge to the optimal solution.