Quantum thermometry in diffraction-limited systems
Dong Xie, Chunling Xu, An Min Wang · Physical Review A · 2022
We investigate the ultimate quantum limit of resolving the temperatures of two thermal sources affected by diffraction. More quantum Fisher information can be obtained with a priori information than without a priori information. We carefully consider two strategies: simultaneous estimation and individual estimation. We prove that the simultaneous estimation of two temperatures satisfies the saturation condition of the quantum Cram\'er-Rao bound and performs better than the individual estimation in the case of a small degree of diffraction given the same resources. However, in the case of a high degree of diffraction, the individual estimation performs better. In particular, at the maximum diffraction, the simultaneous estimation cannot 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 using the full Hermite-Gauss basis can saturate the quantum Cram\'er-Rao bound without being affected by the attenuation factor at the maximum diffraction.