General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology

TL;DR

This paper introduces a comprehensive framework to determine the fundamental limits of measurement precision in noisy quantum systems, revealing how quantum advantages diminish with increasing resources and noise.

Contribution

It provides a general method to derive attainable lower bounds on precision in noisy quantum metrology, applicable to various physical systems and noise models.

Findings

Captures the transition from quantum-enhanced to classical scaling in noisy systems

Applies the bound to optical interferometry and atomic spectroscopy

Shows the bound's independence from initial probe states and adaptive feedback

Abstract

The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). Typically, it scales as 1/N^(1/2). Quantum strategies may improve the precision, for noiseless processes, by an extra factor 1/N^(1/2). For noisy processes, it is not known in general if and when this improvement can be achieved. Here we propose a general framework for obtaining attainable and useful lower bounds for the ultimate limit of precision in noisy systems. We apply this bound to lossy optical interferometry and atomic spectroscopy in the presence of dephasing, showing that it captures the main features of the transition from the 1/N to the 1/N^(1/2) behaviour as N increases, independently of the initial state of the probes, and even with use of adaptive feedback.