Universal algorithm for optimal estimation of quantum states from finite ensembles via realizable generalized measurement

We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable (i.e., finite) positive operator-valued measurement on a finite number of identically prepared systems. We illustrate the general formalism by applying it to different scenarios of the state estimation of N independent and identically prepared two-level systems (qubits).