Metrology with Unknown Detectors

TL;DR

This paper introduces a data fitting pattern approach to estimate the Cramér-Rao bound for unknown detectors, applicable in classical and quantum metrology, simplifying detector characterization and improving precision estimation.

Contribution

It presents a novel, simplified method for estimating the Cramér-Rao bound with unknown detectors using data fitting patterns, applicable to both classical and quantum systems.

Findings

Effective estimation of the Cramér-Rao bound with unknown detectors.

Application to polarimetry demonstrates practical utility.

Formalism aids in quantum harmonic oscillator parameter estimation.

Abstract

The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been introduced in the context of quantum technologies, but apply as well for ordinary classical coherence; these techniques, though, rely on intense data processing. Here we show that one can make use of the simpler approach of data fitting patterns in order to obtain an estimate of the Cram\'er-Rao bound allowed by an unknown detector, and present applications in polarimetry. Further, we show how this formalism provide a useful calculation tool in an estimation problem involving a continuous-variable quantum state, i.e. a quantum harmonic oscillator.