Evaluating the quantum optimal biased bound in a unitary evolution process

TL;DR

This paper introduces two new error bounds for biased estimators in quantum parameter estimation, providing practical guidance for determining the precision limits in unitary evolution processes.

Contribution

It develops and demonstrates two effective biased error bounds within the quantum optimal biased bound framework for unitary evolution.

Findings

The bounds improve understanding of biased estimator performance.

Application to phase encoding and SU(2) interferometer shows practical relevance.

Guides future quantum precision measurement strategies.

Abstract

Seeking the available precision limit of unknown parameters is a significant task in quantum parameter estimation. One often resorts to the widely utilized quantum Cramer-Rao bound (QCRB) based on unbiased estimators to finish this task. Nevertheless, most actual estimators are usually biased in the limited number of trials. For this reason, we introduce two effective error bounds for biased estimators based on a unitary evolution process in the framework of the quantum optimal biased bound. Furthermore, we show their estimation performance by two specific examples of the unitary evolution process, including the phase encoding and the SU(2) interferometer process. Our findings will provide an useful guidance for finding the precision limit of unknown parameters.