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Variational Principle for Optimal Quantum Controls in Quantum Metrology.

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We developed a method to optimize quantum Fisher information for precise quantum metrology. This approach achieves Heisenberg scaling even with limited controls, crucial for realistic quantum sensing applications.

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Area of Science:

  • Quantum Metrology
  • Quantum Information Science
  • Condensed Matter Physics

Background:

  • Quantum metrology aims to enhance measurement precision beyond classical limits.
  • Quantum Fisher information quantifies the ultimate precision achievable in quantum measurements.
  • Realistic quantum metrology often involves limitations on available control operations.

Purpose of the Study:

  • To develop a variational principle for optimizing quantum controls and initial states.
  • To maximize quantum Fisher information under restricted control sets.
  • To investigate approximate methods for achieving optimal precision in realistic scenarios.

Main Methods:

  • Formulation of a variational principle to determine optimal quantum controls and initial states.
  • Analysis of probe time dependence for optimal parameters under restricted controls.
  • Application of Floquet engineering to approximate restricted control problems with unconstrained ones for time-independent Hamiltonians.

Main Results:

  • The optimal initial state and controls can depend on probe time when controls are limited.
  • Floquet engineering effectively reduces the complexity of optimizing under restricted controls.
  • Heisenberg scaling, a benchmark for precision, is approximately achievable in magnetometry with restricted controls (one- and two-body interactions) in a spin chain with three-body interactions.

Conclusions:

  • The developed variational principle provides a framework for quantum metrology with limited controls.
  • Floquet engineering offers a viable strategy to approach optimal precision in constrained systems.
  • The findings are relevant for advancing many-body quantum metrology in practical experimental settings.