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  • 1Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.

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This study links precision and irreversibility in quantum systems. It reveals that measuring quantum processes with higher precision increases entropy production, unifying classical and quantum thermodynamic uncertainty relations.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Mechanics
  • Information Theory

Background:

  • Entropy production quantifies the irreversibility of thermodynamic processes.
  • The thermodynamic uncertainty relation connects precision and entropy production in classical systems.
  • Understanding these relations in quantum systems is crucial for quantum technologies.

Purpose of the Study:

  • To establish a unified perspective on thermodynamic uncertainty relations in both classical and quantum regimes.
  • To investigate the relationship between precision of measurements and irreversibility in quantum Markov processes.
  • To introduce a novel bound for the precision of counting observables in continuous quantum measurements.

Main Methods:

  • Analysis of original and perturbed quantum dynamics.
  • Application of continuous measurement theory for quantum Markov processes.
  • Derivation of a lower bound for precision based on the Loschmidt echo.

Main Results:

  • The precision of arbitrary counting observables in continuous quantum measurements is bounded below by the Loschmidt echo.
  • This bound directly relates measurement precision to the irreversibility of quantum dynamics.
  • Specific perturbed dynamics yield known thermodynamic uncertainty relations, demonstrating a unified framework.

Conclusions:

  • The proposed relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.
  • The Loschmidt echo serves as a measure of irreversibility bounding quantum measurement precision.
  • This work deepens the understanding of fundamental trade-offs between information and thermodynamics in quantum systems.