Efficient quantum-state estimation by continuous weak measurement and dynamical control

We demonstrate a fast, robust, and nondestructive protocol for quantum-state estimation based on continuous weak measurement in the presence of a controlled dynamical evolution. Our experiment uses optically probed atomic spins as a test bed and successfully reconstructs a range of trial states with fidelities of ∼90%. The procedure holds promise as a practical diagnostic tool for the study of complex quantum dynamics, the testing of quantum hardware, and as a starting point for new types of quantum feedback control.