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. 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. 
A. Smith, C. A. Riofr\'io, B. E. Anderson, H. Sosa-Martinez, I. H.   Deutsch, and P. S. Jessen
quant-ph