Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance--optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically the performances of two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.