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Quantum metrology with imperfect measurements.

Yink Loong Len1,2, Tuvia Gefen3, Alex Retzker4,5

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Measurement imperfections in quantum metrology are systematically addressed. Global control operations recover ideal sensitivity, while local operations offer limited quantum enhancement for noisy quantum Fisher information.

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Area of Science:

  • Quantum Metrology
  • Quantum Information Science
  • Measurement Science

Background:

  • Measurement imperfections pose a significant challenge in quantum metrology.
  • A systematic approach to understanding these imperfections is lacking.

Purpose of the Study:

  • To generalize quantum Fisher information for noisy detection.
  • To develop methods for approximate evaluation of noisy quantum Fisher information.
  • To analyze the impact of control operations on sensitivity in the presence of measurement noise.

Main Methods:

  • Generalization of quantum Fisher information to include readout noise.
  • Development of tractable methods for approximate evaluation.
  • Analysis of local vs. global control operations in canonical N-probe scenarios.

Main Results:

  • Optimal sensitivity critically depends on control operations balancing measurement imperfections.
  • Global control operations can recover Heisenberg scaling in the asymptotic limit.
  • Local control operations constrain quantum enhancement to a constant factor.

Conclusions:

  • The study provides a framework for understanding and mitigating measurement imperfections in quantum metrology.
  • Specific examples like NV-center magnetometry and spin-1/2 probes demonstrate practical applications.
  • Optimal input states and control operations are identified for achieving ultimate precision.