# Information Scrambling and Loschmidt Echo

## TL;DR

This paper establishes an analytical and numerical connection between the out-of-time-order correlator, a measure of quantum information scrambling, and the Loschmidt echo, a classical diagnostic of chaos, enhancing experimental accessibility.

## Contribution

It reveals a direct relationship between the out-of-time-order correlator and the Loschmidt echo, linking quantum information scrambling to a well-known dynamical chaos measure.

## Key findings

- Analytical demonstration of the correlator-echo relationship
- Numerical verification confirming the theoretical link
- Provides a practical approach for experimental studies of quantum chaos

## 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.