Information Scrambling and Loschmidt Echo.

@article{Yan2020InformationSA,
  title={Information Scrambling and Loschmidt Echo.},
  author={Bin Yan and Lukasz Cincio and Wojciech Zurek},
  journal={Physical review letters},
  year={2020},
  volume={124 16},
  pages={
          160603
        }
}
We demonstrate analytically and verify numerically that the out-of-time order correlator is given by the thermal average of Loschmidt echo signals. This provides a direct link between the out-of-time-order correlator-a recently suggested measure of information scrambling in quantum chaotic systems-and the Loschmidt echo, a well-appreciated familiar diagnostic that captures the dynamical aspect of chaotic behavior in the time domain, and is accessible to experimental studies. 

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