Quantum speed limit for the out-of-time-ordered correlator from an open-system perspective

Abstract

Scrambling, the delocalization of initially localized quantum information, is commonly characterized by the out-of-time-ordered correlator (OTOC). Employing the OTOC–Renyi-2 entropy theorem, we derive a quantum speed limit for the OTOC, which sets a lower bound for the rate with which information can be scrambled. This bound becomes particularly tractable by describing the scrambling of information in a closed quantum system as an effective decoherence process of an open system interacting with an environment. We prove that decay of the OTOC can be bounded by the strength of the system-environment coupling and two-point environmental correlation functions. We validate our analytic bound numerically using the nonintegrable transverse field Ising model. Our results provide a universal and model-agnostic quantitative framework for understanding the dynamical limits of information spreading across quantum many-body physics, condensed matter systems, and engineered quantum platforms.