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Quantum Metrology for Non-Markovian Processes.

Anian Altherr1, Yuxiang Yang1,2

  • 1Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland.

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This study introduces a framework for non-Markovian quantum metrology, offering a new approach to quantum channel estimation. The research finds improved quantum metrology performance in non-Markovian systems compared to Markovian ones.

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Area of Science:

  • Quantum Information Science
  • Quantum Technologies
  • Quantum Metrology

Background:

  • Quantum metrology theories are well-developed for Markovian processes.
  • Quantum metrology for non-Markovian processes remains significantly less explored.
  • This gap limits the application of quantum metrology in complex, realistic systems.

Purpose of the Study:

  • To establish a general theoretical framework for non-Markovian quantum metrology.
  • To derive a formula for maximal quantum Fisher information extraction in non-Markovian processes.
  • To develop a computational method for evaluating this information.

Main Methods:

  • Development of a general framework for non-Markovian quantum metrology.
  • Derivation of a formula for maximal quantum Fisher information for parametrized non-Markovian processes.
  • Design of an algorithm utilizing semidefinite programming for evaluation.
  • Application to noisy frequency estimation.

Main Results:

  • A general framework for non-Markovian quantum metrology is established.
  • A formula for maximal quantum Fisher information extraction is derived.
  • An algorithm for evaluating quantum Fisher information via semidefinite programming is presented.
  • Noisy frequency estimation shows superior performance in non-Markovian scenarios.

Conclusions:

  • The developed framework advances quantum metrology for non-Markovian systems.
  • Non-Markovian quantum metrology offers enhanced performance over Markovian approaches.
  • Efficient sensing is possible using simple variational circuits within this framework.