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

TL;DR

This paper introduces an adaptive measurement strategy for 1-qubit state estimation using an A-optimality criterion, providing more precise results than traditional methods with finite data.

Contribution

It applies a classical optimal experimental design criterion to quantum state estimation and derives an analytic solution for 1-qubit measurements, reducing computational complexity.

Findings

Adaptive scheme outperforms nonadaptive methods in accuracy

Analytic solution simplifies the A-optimality calculation

Adaptive measurements improve estimation precision with finite data

Abstract

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.