Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion
This addresses the challenge of improving quantum state estimation efficiency for quantum computing applications, but it is incremental as it builds on classical experimental design methods.
The paper tackled the problem of estimating a one-qubit mixed quantum state with finite data by adaptively updating measurements based on an A-optimality criterion, resulting in more precise estimates than standard quantum tomography as shown numerically.
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 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.