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Quantum metrological limits via a variational approach.

B M Escher1, L Davidovich, N Zagury

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, 21.941-972 Rio de Janeiro, Brazil. bmescher@if.ufrj.br

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Summary
This summary is machine-generated.

We derived a new method to calculate quantum Fisher information in noisy systems. This quantum precision estimation provides a noise-dependent bound for phase-shift measurements.

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Area of Science:

  • Quantum information science
  • Quantum metrology
  • Statistical estimation theory

Background:

  • The quantum Fisher information (QFI) sets the ultimate limit on parameter estimation precision.
  • Calculating QFI for noisy quantum systems remains a significant challenge.

Purpose of the Study:

  • To develop a robust method for computing QFI in the presence of noise.
  • To establish an analytical bound for quantum precision in phase-shift estimation under phase diffusion.

Main Methods:

  • A variational approach was employed to derive an equation for QFI.
  • The equation explicitly incorporates the mathematical model of noise.
  • The method was applied to phase-shift estimation with phase diffusion.

Main Results:

  • An equation for QFI with explicit noise dependence was obtained.
  • An analytical bound for quantum precision in phase-shift estimation was derived.
  • The study demonstrates that estimation uncertainty has a noise-dependent lower limit.

Conclusions:

  • The presented variational method offers a tractable way to compute QFI for noisy systems.
  • The derived bound provides crucial insights into the limitations imposed by phase diffusion on quantum precision.
  • This work advances the understanding of quantum metrology in realistic noisy environments.