A geometric perspective: experimental evaluation of the quantum Cramer-Rao bound

TL;DR

This paper investigates the fundamental limits of multi-parameter quantum sensing using quantum geometry, experimentally evaluating the quantum Cramer-Rao bound and revealing how quantum incompatibility affects achievable precision.

Contribution

It introduces a geometric approach to experimentally evaluate the quantum Cramer-Rao bound in multi-parameter quantum estimation, highlighting the role of quantum incompatibility.

Findings

Quantum geometry measurements can evaluate the QCRB.

Quantum incompatibility prevents saturation of the QCRB.

The geometric 'quantumness' metric links to estimation precision.

Abstract

The power of quantum sensing rests on its ultimate precision limit, quantified by the quantum Cramer-Rao bound (QCRB), which can surpass classical bounds. In multi-parameter estimation, the QCRB is not always saturated as the quantum nature of associated observables may lead to their incompatibility. Here we explore the precision limits of multi-parameter estimation through the lens of quantum geometry, enabling us to experimentally evaluate the QCRB via quantum geometry measurements. Focusing on two- and three-parameter estimation, we elucidate how fundamental quantum uncertainty principles prevent the saturation of the bound. By linking a metric of "quantumness" to the system geometric properties, we investigate and experimentally extract the attainable QCRB for three-parameter estimations.