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Distinguish between typical non-Hermitian quantum systems by entropy dynamics.

Chao Zheng1, Daili Li2

  • 1Department of Physics, College of Science, North China University of Technology, Beijing, 100144, People's Republic of China. czheng@ncut.edu.cn.

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Summary

Entropy dynamics can distinguish phases of non-Hermitian (NH) quantum systems. This method uses quantum decoherence and projective measurements, avoiding quantum tomography for phase transition detection in NH systems.

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Area of Science:

  • Quantum Physics
  • Condensed Matter Theory
  • Quantum Information Science

Background:

  • Non-Hermitian (NH) quantum systems, including PT-symmetric and pseudo-Hermitian variants, are gaining significant research attention.
  • Distinguishing different phases and time-evolutions in NH systems remains a key challenge.

Purpose of the Study:

  • To extend the application of entropy dynamics for classifying NH quantum systems.
  • To investigate entropy evolution after quantum decoherence induced by projective measurements in two-level NH systems.
  • To develop a method for distinguishing all eight phases of NH systems without quantum tomography.

Main Methods:

  • Investigated entropy dynamics in two-level NH systems subjected to quantum decoherence via single-qubit projective measurements.
  • Analyzed the dependence of entropy evolution on initial states and measurement computational bases.
  • Proposed a step-by-step phase distinguishing protocol requiring three initial states for a fixed measurement basis.

Main Results:

  • Entropy dynamics were found to depend on both initial states and measurement bases.
  • A general method was demonstrated to distinguish all eight phases of NH systems.
  • The proposed method for distinguishing phases does not require quantum tomography, making it suitable for quantum simulations.

Conclusions:

  • Entropy dynamics provide a robust tool for classifying phases and time-evolutions in non-Hermitian systems.
  • The developed method offers a practical approach for identifying phase transitions in NH systems through quantum simulation.
  • This work contributes to a deeper understanding of the rich phase structures in non-Hermitian quantum mechanics.