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π-Corrected Heisenberg Limit.

Wojciech Górecki1, Rafał Demkowicz-Dobrzański1, Howard M Wiseman2

  • 1Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.

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|February 8, 2020
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Summary
This summary is machine-generated.

This study establishes a new lower bound for estimating the parameter φ in quantum systems. The derived bound surpasses the conventional Heisenberg limit, offering improved precision in quantum measurements.

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Area of Science:

  • Quantum Information Science
  • Quantum Metrology
  • Parameter Estimation

Background:

  • Accurate estimation of parameters is crucial in quantum technologies.
  • The Heisenberg limit provides a benchmark for quantum measurement precision.
  • Existing methods face limitations with finite prior information.

Purpose of the Study:

  • To determine a fundamental lower bound for parameter estimation precision.
  • To investigate the impact of finite prior information on quantum sensing.
  • To establish a new precision limit beyond the conventional Heisenberg limit.

Main Methods:

  • Analysis of unitary transformations U_{φ}=e^{iφΛ} acting on probe systems.
  • Asymptotic analysis for a large number of operations (n).
  • Derivation of a tight lower bound for precision Δφ.

Main Results:

  • A novel lower bound for precision is derived: Δφ≥π/[n(λ_{+}-λ_{-})].
  • This bound is asymptotically tight for large n.
  • The new bound exceeds the conventional Heisenberg limit by a factor of π.

Conclusions:

  • The conventional Heisenberg limit derived from quantum Fisher information is not always saturable.
  • The established bound is universally applicable, regardless of measurement protocol.
  • The findings are relevant for both noiseless scenarios and those with correctable noise.