Fast state tomography with optimal error bounds
Guta, M., Jonas Kahn, Richard Kueng, Joel A. Tropp · CaltechAUTHORS (California Institute of Technology) · 2020
Projected least squares is an intuitive and numerically cheap technique for quantum state tomography: compute the least-squares estimator and project it onto the space of states. The main result of this paper equips this point estimator with rigorous, non-asymptotic convergence guarantees expressed in terms of the trace distance. The estimator's sample complexity is comparable to the strongest convergence guarantees available in the literature and—in the case of the uniform POVM—saturates fundamental lower bounds. Numerical simulations support these competitive features.