Assessing data postprocessing for quantum estimation

TL;DR

This paper reviews strategies for optimizing quantum sensors, focusing on the importance of data postprocessing and estimator selection to reach ultimate measurement precision, and analyzes the information content of standard bounds.

Contribution

It provides a comprehensive review of methods for finding optimal estimators in quantum sensing and explores the informational completeness of standard bounds.

Findings

Most information is conveyed by standard bounds.

Higher-order moments offer limited additional insight.

Strategies for estimator optimization are crucial for quantum sensor performance.

Abstract

Quantum sensors are among the most promising quantum technologies, allowing to attain the ultimate precision limit for parameter estimation. In order to achieve this, it is required to fully control and optimize what constitutes the hardware part of the sensors, i.e. the preparation of the probe states and the correct choice of the measurements to be performed. However careful considerations must be drawn also for the software components: a strategy must be employed to find a so-called optimal estimator. Here we review the most common approaches used to find the optimal estimator both with unlimited and limited resources. Furthermore, we present an attempt at a more complete characterization of the estimator by means of higher-order moments of the probability distribution, showing that most information is already conveyed by the standard bounds.