Quantum state tomography by continuous measurement and compressed sensing

A. Smith, C. A. Riofrío, B. E. Anderson, H. Sosa-Martinez, I. H. Deutsch, P. S. Jessen

Published 2012-08-24, updated 2013-03-14Version 2

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.