Multi-outcome homodyne detection in a coherent-state light interferometer.

Area of Science:

• Quantum estimation theory
• Quantum optics
• Interferometry

Background:

• The Cramér-Rao bound is crucial for parameter estimation but achieving it is challenging for multi-outcome measurements.
• Optimal observables and inversion estimators for saturating the bound are not generally known.

Purpose of the Study:

• To construct inversion estimators that approach the Cramér-Rao bound for multi-outcome measurements.
• To address the open issue of achieving the bound in general parameter estimation scenarios.

Main Methods:

• Utilizing multi-outcome homodyne detection in a coherent-light Mach-Zehnder interferometer.
• Developing a family of inversion estimators designed to saturate the Cramér-Rao bound.

Main Results:

• Demonstrated inversion estimators that almost saturate the Cramér-Rao bound across the entire phase interval.
• Showcased the effectiveness of the proposed methods in a practical interferometric setup.

Conclusions:

• The developed estimators offer a pathway to optimal phase estimation in multi-outcome measurements.
• This work provides insights for constructing optimal estimators in broader parameter estimation contexts.