Quantum state tomography by continuous measurement and compressed sensing

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. They both efficiently reconstruct nearly pure states in the 16-dimensional ground manifold, reaching average fidelities F̄CS=0.92 and F̄LS=0.88 using similar amounts of incomplete data. Surprisingly, the main advantage of CS in our protocol is an increased robustness to experimental imperfections.