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Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert-Schmidt Speed-Based Witness.

Kobra Mahdavipour1,2, Mahshid Khazaei Shadfar1,2, Hossein Rangani Jahromi3

  • 1Dipartimento di Ingegneria, Università di Palermo, Viale delle Scienze, 90128 Palermo, Italy.

Entropy (Basel, Switzerland)
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Summary

A new method using Hilbert-Schmidt speed (HSS) reliably detects non-Markovianity in complex quantum systems. This witness is easy to compute and accurately tracks memory effects in quantum evolution.

Keywords:
Hilbert–Schmidt speedhigh-dimensional systemmemory effectsmultipartite open quantum systemsnon-Markovianity

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Area of Science:

  • Quantum Information Science
  • Quantum Dynamics
  • Open Quantum Systems

Background:

  • Non-Markovianity describes memory effects in quantum systems, crucial for understanding quantum evolution.
  • A Hilbert-Schmidt speed (HSS)-based witness for non-Markovianity was recently developed for low-dimensional systems.
  • This HSS witness is computationally efficient as it avoids density matrix diagonalization.

Purpose of the Study:

  • To assess the effectiveness of the HSS-based witness in detecting non-Markovianity.
  • To evaluate the HSS witness's performance in high-dimensional and multipartite open quantum systems with finite Hilbert spaces.

Main Methods:

  • Investigated the time evolution of the HSS-based witness.
  • Compared the HSS witness's behavior with established measures like quantum negativity and quantum correlation.
  • Analyzed various high-dimensional and multipartite open quantum systems.

Main Results:

  • The HSS-based witness successfully detected non-Markovianity in the studied systems.
  • The time evolution of the HSS witness consistently aligned with quantum negativity and quantum correlation measures.
  • The witness proved effective even in complex, high-dimensional quantum scenarios.

Conclusions:

  • The HSS-based witness is a reliable tool for identifying non-Markovian dynamics.
  • This method is suitable for analyzing memory effects in high-dimensional, finite Hilbert space quantum systems.
  • The computational simplicity of the HSS witness enhances its practical applicability in quantum information science.