Quantum thermometry in diffraction-limited systems

TL;DR

This paper explores the fundamental quantum limits of temperature resolution in diffraction-limited systems, comparing simultaneous and individual estimation strategies, and identifies optimal measurement approaches under various diffraction conditions.

Contribution

It introduces a comprehensive analysis of quantum thermometry strategies, revealing conditions where simultaneous or individual estimation is optimal, and proposes practical measurement methods using Hermite-Gauss basis.

Findings

Simultaneous estimation outperforms individual estimation at low diffraction.

Individual estimation remains effective at high diffraction levels.

Hermite-Gauss basis measurements saturate the quantum Cramér-Rao bound at maximum diffraction.

Abstract

We investigate the ultimate quantum limit of resolving the temperatures of two thermal sources affected by the diffraction. More quantum Fisher information can be obtained with the priori information than that without the priori information. We carefully consider two strategies: the simultaneous estimation and the individual estimation. The simultaneous estimation of two temperatures is proved to satisfy the saturation condition of quantum Cram\'{e}r bound and performs better than the individual estimation in the case of small degree of diffraction given the same resources. However, in the case of high degree of diffraction, the individual estimation performs better. In particular, at the maximum diffraction, the simultaneous estimation can not get any information, which is supported by a practical measurement, while the individual estimation can still get the information. In addition, we find that for the individual estimation, a practical and feasible estimation strategy by using the full Hermite-Gauss basis can saturate the quantum Cram\'{e}r bound without being affected by the attenuation factor at the maximum diffraction. using the full Hermite-Gauss basis can saturate the quantum Cram\'er bound without being affected by the attenuation factor at the maximum diffraction.