Semiclassical Approach to Quantum Fisher Information

Area of Science:

• Quantum physics
• Quantum chaos
• Quantum sensing

Background:

• Quantum chaotic systems offer enhanced sensitivity for quantum sensors.
• Sensitivity is intricately linked to the classical phase space details.
• Quantifying ultimate sensitivity requires understanding quantum Fisher information (QFI).

Purpose of the Study:

• To develop an accurate semiclassical approach for accessing phase-space-resolved QFI.
• To establish a direct link between QFI and classical dynamical quantities.
• To demonstrate the method's applicability and accuracy in quantum chaos systems.

Main Methods:

• Development of a novel semiclassical approximation.
• Calculation of phase-space-resolved quantum Fisher information (QFI).
• Application to the kicked top model, a paradigmatic quantum chaos system.

Main Results:

• The semiclassical approach provides efficient access to phase-space-resolved QFI.
• High QFI is correlated with large variance in a specific dynamical quantity.
• The method shows high accuracy for modest quantum numbers, deep in the quantum regime.

Conclusions:

• The developed semiclassical method accurately predicts quantum sensor sensitivity.
• It reveals a clear connection between quantum sensitivity and classical phase space dynamics.
• The approach is scalable to very high quantum numbers, surpassing limitations of other methods.