Abstract

The process by which initially localized quantum information in a system is rendered irretrievable due to quantum dynamics, referred to as ‘scrambling’, has been a subject of intense interest in the last decade. The out-of-time-ordered correlators (OTOCs) form an important class of quantitative tools that yield Lyapunov exponents which quantify the rate of scrambling in quantum systems. The rate of scrambling of quantum information in thermal quantum systems, as quantified using these Lyapunov exponents, is conjectured to obey a temperature-dependent universal quantum bound. Our numerical investigation on a model chaotic system strongly suggests that, at least in quantum-Boltzmann ensembles, the bound on the Lyapunov exponent is purely a quantum-statistical effect, which can be explained using imaginary-time Feynman path-integrals. Specifically, we find that delocalized structures in a fictitious extended phase space that represent bounce instantons are responsible for this bound.