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.
@article{arxiv.1208.5015,
title = {Quantum state tomography by continuous measurement and compressed sensing},
author = {A. Smith and C. A. Riofrío and B. E. Anderson and H. Sosa-Martinez and I. H. Deutsch and P. S. Jessen},
journal= {arXiv preprint arXiv:1208.5015},
year = {2013}
}