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Frequentist and Bayesian Quantum Phase Estimation.

Yan Li1, Luca Pezzè2, Manuel Gessner2

  • 1Institute of Theoretical Physics and Department of Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China.

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Summary
This summary is machine-generated.

Frequentist and Bayesian approaches yield different knowledge states for parameter estimation. Bayesian variance can surpass the frequentist Cramér-Rao bound, highlighting conceptual distinctions in quantum phase estimation.

Keywords:
Bayesian estimationparameter estimationquantum metrology

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Area of Science:

  • Quantum optics
  • Statistical inference
  • Metrology

Background:

  • Frequentist and Bayesian frameworks offer distinct perspectives on parameter estimation and knowledge representation.
  • Quantum noise limits precision in interferometric phase shift estimation, a critical task in metrology.

Purpose of the Study:

  • To compare frequentist and Bayesian phase estimation strategies and their sensitivity bounds.
  • To analyze the estimation of both fixed and fluctuating interferometric phase shifts under quantum noise.

Main Methods:

  • Comparative analysis of frequentist (e.g., Cramér-Rao bound) and Bayesian sensitivity bounds.
  • Investigation of phase estimation for both static and dynamic interferometric parameters.

Main Results:

  • Frequentist and Bayesian precision bounds are not interchangeable; each has limitations.
  • Bayesian variance can outperform the frequentist Cramér-Rao bound, a key finding when conceptual differences are considered.
  • Bounds for fluctuating parameters do not apply to fixed parameter estimation.

Conclusions:

  • The conceptual divergence between frequentist and Bayesian methods is crucial for understanding parameter estimation bounds.
  • Bayesian strategies offer potential advantages in precision for quantum phase estimation, challenging traditional frequentist limits.
  • Distinct bounds are required for fixed versus fluctuating parameter estimation scenarios.