Abstract
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 Cramér-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 Cramér-Rao bound without being affected by the attenuation factor at the maximum diffraction.
1 More- Received 17 August 2022
- Accepted 26 October 2022
DOI:https://doi.org/10.1103/PhysRevA.106.052407
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