Information Scrambling and Loschmidt Echo

Phys Rev Lett. 2020 Apr 24;124(16):160603. doi: 10.1103/PhysRevLett.124.160603.

Abstract

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.