Valid lower bound for all estimators in quantum parameter estimation

TL;DR

This paper introduces a universal lower bound for all estimators in quantum parameter estimation, providing a more accurate benchmark than the traditional quantum Cramer-Rao bound, especially for limited measurements.

Contribution

The authors propose a new lower bound applicable to both biased and unbiased estimators, improving the evaluation of quantum estimation performance beyond existing bounds.

Findings

The new bound is valid for all estimators regardless of bias.

It offers a more accurate performance benchmark in limited measurement scenarios.

The bound generalizes the quantum Cramer-Rao bound to finite measurement regimes.

Abstract

The widely used quantum Cramer-Rao bound (QCRB) sets a lower bound for the mean square error of unbiased estimators in quantum parameter estimation, however, in general QCRB is only tight in the asymptotical limit. With a limited number of measurements biased estimators can have a far better performance for which QCRB cannot calibrate. Here we introduce a valid lower bound for all estimators, either biased or unbiased, which can serve as standard of merit for all quantum parameter estimations.