Review Reports

Round 1

Reviewer 1 Report

The paper discusses generalization of OTOC and provides novel bounds on the "Lyapunov exponents" controlling the exponential growth of the generalized OTOC correlators. These new correlators give access of the statistical distribution of the Lyapunov exponents associated with different initial conditions (different trajectories). The paper is well written, it will be of interest to a broad community working on various aspects of quantum chaos and I recommend it for publication. 

Reviewer 2 Report

This is an interesting and important paper that usefully generalizes known results on the exponential growth rates of certain "out of time order" quantum correlation functions. The authors study these correlation functions both analytically and numerically, and place new bounds on the growth rate of high powers of the commutator of two operators at two different times, which in turn places limits on the size of large deviations. The research and the presentation are both very well done.