Optimal Quantum Metrology of Distant Black Bodies

TL;DR

This paper develops the quantum optimal estimation methods for determining the temperature and spatial configuration of distant black bodies using far-field radiation, advancing quantum metrology in astrophysical and engineering contexts.

Contribution

It introduces the first quantum optimal estimators for temperature and imaging of distant objects, addressing multi-parameter quantum estimation of incompatible observables.

Findings

Optimal estimators minimize the cost function weighted by quantum Fisher information.

Separable quantum measurements outperform classical two-mode analogues in imaging.

The proposed estimators maximize the fidelity between true and estimated quantum states.

Abstract

Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body based on the black body radiation received in the far-field. We also show how to perform separable quantum optimal estimates of the spatial configuration of a distant object, i.e. imaging. In doing so we necessarily deal with multi-parameter quantum estimation of incompatible observables, a problem that is poorly understood. We compare our optimal observables to the two mode analogue of lensed imaging and find that the latter is far from optimal, even when compared to measurements which are separable. To prove the optimality of the estimators we show that they minimise the cost function weighted by the quantum Fisher information---this is equivalent to maximising the average fidelity between the actual state and the estimated one.