Bayesian error regions in quantum estimation II: region accuracy and adaptive methods

TL;DR

This paper introduces the concept of region accuracy in Bayesian quantum estimation, proposing adaptive methods to optimize error regions and demonstrating their effectiveness through quantum-parameter estimation examples.

Contribution

It defines region accuracy for Bayesian error regions and develops adaptive procedures to maximize this accuracy based solely on the observed data.

Findings

Adaptive methods outperform nonadaptive procedures in quantum estimation examples.

Region accuracy increases with adaptive strategies, improving error region quality.

The approach generalizes point-estimator accuracy to entire error regions in quantum estimation.

Abstract

Bayesian error analysis paves the way to the construction of credible and plausible error regions for a point estimator obtained from a given dataset. We introduce the concept of region accuracy for error regions (a generalization of the point-estimator mean squared-error) to quantify the average statistical accuracy of all region points with respect to the unknown true parameter. We show that the increase in region accuracy is closely related to the Bayesian-region dual operations in [1]. Next with only the given dataset as viable evidence, we establish various adaptive methods to maximize the region accuracy relative to the true parameter subject to the type of reported Bayesian region for a given point estimator. We highlight the performance of these adaptive methods by comparing them with nonadaptive procedures in three quantum-parameter estimation examples. The results of and mechanisms behind the adaptive schemes can be understood as the region analog of adaptive approaches to achieving the quantum Cramer--Rao bound for point estimators.