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Information Scrambling and Loschmidt Echo.

Bin Yan1,2,3, Lukasz Cincio1, Wojciech H Zurek1

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|May 9, 2020
PubMed
Summary
This summary is machine-generated.

We found that the out-of-time-order correlator, a measure of quantum information scrambling, is equivalent to the thermal average of Loschmidt echo signals. This links quantum chaos diagnostics and experimental measures.

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Area of Science:

  • Quantum Physics
  • Statistical Mechanics
  • Chaos Theory

Background:

  • The out-of-time-order correlator (OTOC) is a key metric for quantifying information scrambling in quantum chaotic systems.
  • The Loschmidt echo is a well-established diagnostic tool in quantum dynamics, sensitive to chaotic behavior.

Purpose of the Study:

  • To establish a direct analytical and numerical link between the out-of-time-order correlator and the Loschmidt echo.
  • To connect a novel measure of quantum chaos (OTOC) with an experimentally accessible quantity (Loschmidt echo).

Main Methods:

  • Analytical derivation demonstrating the equivalence.
  • Numerical verification of the derived relationship.

Main Results:

  • The out-of-time-order correlator is shown to be equal to the thermal average of Loschmidt echo signals.
  • A direct quantitative relationship between OTOC and Loschmidt echo is established.

Conclusions:

  • This work bridges theoretical concepts of quantum information scrambling with experimental observables.
  • The findings facilitate the study of quantum chaos through accessible experimental measurements of the Loschmidt echo.