Quantum Fisher information for estimating N partially coherent point sources

Area of Science:

• Quantum optics
• Metrology
• Information theory

Background:

• Estimating localization parameters of objects is crucial in various scientific fields.
• Partial coherence in quantum objects can influence measurement precision.
• Understanding quantum Fisher information is key for high-precision measurements.

Purpose of the Study:

• To theoretically demonstrate that partially coherent objects can be localized with higher precision than incoherent objects.
• To determine the maximum number of independent parameters with non-vanishing precision in the sub-Rayleigh regime for partially coherent objects.
• To introduce and detail normalization schemes for interpreting quantum Fisher information in the presence of partial coherence.

Main Methods:

• Theoretical analysis of localization precision for partially coherent and incoherent objects.
• Investigation of parameter estimation in the sub-Rayleigh regime.
• Development and explanation of normalization schemes for quantum Fisher information.

Main Results:

• Partially coherent objects allow for theoretically higher precision in localization parameter estimation compared to incoherent objects.
• The maximum number of independent parameters with non-vanishing precision in the sub-Rayleigh regime is 3 for partially coherent objects, versus 2 for incoherent objects.
• Normalization schemes are presented as essential for accurate interpretation of quantum Fisher information with partial coherence.

Conclusions:

• Partial coherence enhances the precision of object localization, particularly in the sub-Rayleigh regime.
• The findings provide a theoretical framework for improved quantum metrology using partially coherent states.
• Proper normalization is critical for reliable quantum Fisher information analysis in partially coherent systems.