Quantum state tomography by continuous measurement and compressed sensing

TL;DR

This paper compares compressed sensing and least squares methods for quantum state tomography using continuous measurements on cesium atomic spins, highlighting compressed sensing's robustness to imperfections.

Contribution

It demonstrates that compressed sensing can efficiently reconstruct nearly pure quantum states with higher robustness than least squares in a continuous measurement protocol.

Findings

Compressed sensing achieves an average fidelity of 0.92.

Least squares achieves an average fidelity of 0.88.

Compressed sensing shows increased robustness to experimental imperfections.

Abstract

The need to perform quantum state tomography on ever larger systems has spurred a search for methods that yield good estimates from incomplete data. We study the performance of compressed sensing (CS) and least squares (LS) estimators in a fast protocol based on continuous measurement on an ensemble of cesium atomic spins. Both efficiently reconstruct nearly pure states in the 16-dimensional ground manifold, reaching average fidelities FCS = 0.92 and FLS = 0.88 using similar amounts of incomplete data. Surprisingly, the main advantage of CS in our protocol is an increased robustness to experimental imperfections.