Joint estimation of phase and phase diffusion for quantum metrology.

Area of Science:

• Quantum information science
• Quantum metrology and sensing

Background:

• Quantum phase estimation is crucial for metrology and communication but is sensitive to unknown or drifting noise.
• Accurate estimation of both phase shifts and noise amplitude is essential for robust quantum technologies.

Purpose of the Study:

• To investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit.
• To derive a trade-off bound for the statistical variances in multiparameter quantum estimation.
• To identify optimal measurement schemes for joint parameter estimation.

Main Methods:

• Reshaping the multiparameter estimation problem into a two-dimensional Hilbert space model.
• Analyzing quantum interferometry with various quantum states: split single-photons, coherent states, and N00N states.
• Deriving a trade-off bound on statistical variances for joint phase and phase diffusion estimation.

Main Results:

• A fundamental trade-off bound was established for the joint estimation of phase and phase diffusion.
• Optimal measurement schemes were identified for specific quantum states.
• The derived bound was used to quantify the performance of an experimental polarimetry setup.

Conclusions:

• The study provides a theoretical framework and practical guidelines for joint parameter estimation in the presence of noise.
• The findings are applicable to improving the precision of quantum metrology and sensing applications.
• The trade-off relations offer insights into the limitations and possibilities for general quantum states and measurements.