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This study introduces information-theoretic quantum metrology, focusing on recovered parameter bits instead of precision. It redefines quantum metrology benchmarks, showing entanglement is key for optimal strategies.

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Area of Science:

  • Quantum physics
  • Information theory
  • Metrology

Background:

  • Quantum metrology traditionally quantifies precision using root-mean-square error (RMSE) and Fisher information.
  • Existing benchmarks like the Heisenberg bound and standard quantum limit guide quantum estimation theory.

Purpose of the Study:

  • To develop an information-theoretic framework for quantum metrology.
  • To determine the number of parameter bits recoverable through quantum estimation strategies.
  • To redefine and analyze quantum metrology benchmarks within an information-theoretic context.

Main Methods:

  • Derivation of an information-theoretic quantum metrology framework.
  • Redefinition of the Heisenberg bound and standard quantum limit.
  • Analysis of different probe strategies: sequential, parallel with entanglement, and parallel-separable.

Main Results:

  • The Heisenberg bound is achievable only with sequential strategies or parallel strategies utilizing entanglement.
  • Parallel-separable strategies are fundamentally limited compared to entangled approaches.
  • Distinct differences are observed between information-theoretic and RMSE-based quantum metrology.

Conclusions:

  • Information-theoretic quantum metrology offers a new perspective on quantifying estimation performance.
  • Entanglement plays a crucial role in achieving optimal parameter estimation in quantum systems.
  • The study provides a refined understanding of fundamental limits in quantum metrology.