Quantum-Limited Loss Sensing: Multiparameter Estimation and Bures Distance between Loss Channels

Area of Science:

• Quantum optics
• Quantum metrology
• Information theory

Background:

• Estimating optical system parameters is crucial for applications like imaging and spectroscopy.
• Current methods face limitations due to environmental interactions and energy constraints.
• Ancilla-assisted parallel strategies offer a theoretical framework for enhanced estimation.

Purpose of the Study:

• To solve the problem of estimating multiple optical loss parameters under energy constraints using a general ancilla-assisted parallel strategy.
• To derive an upper bound on the quantum Fisher information matrix for lossy optical systems.
• To identify optimal probe states and measurement strategies for achieving quantum-optimal parameter estimation.

Main Methods:

• Derivation of an upper bound on the quantum Fisher information matrix.
• Analysis of pure-state probes that are number diagonal in interacting modes.
• Investigation of ancilla-assisted parallel strategies under energy constraints.
• Calculation of the Bures distance between product loss channels.

Main Results:

• An upper bound on the quantum Fisher information matrix is derived for lossy optical systems.
• Pure-state probes achieve this upper bound even when environment modes are inaccessible.
• Parameter-independent optimal measurements using Schmidt bases are identified.
• Quantum-optimal performance is achievable with specific probe states (e.g., squeezed vacuum, single-photon states) and on-off detection.

Conclusions:

• The study provides a theoretical framework for optimal estimation of multiple loss parameters in optical systems.
• Practical implementation is feasible using readily available quantum states and detection methods.
• The findings have significant implications for various optical sensing and measurement applications.