Abstract

Motivated by black hole physics and holography, we study chaos, scrambling, and complexity by considering the entanglement properties of unitary operators. First, we develop a diagnostic of chaos by directly considering the time evolution of a simple local operator. This leads us to out-of-time-order (OTO) four-point functions as an indicator of the strength of the butterfly effect, and we provide a model calculation of such correlators in 1+1-dimensional CFT . Next, we propose and elaborate on the negativity of the tripartite information as a measure of the information-theoretic notion of scrambling. By taking an average of OTO correlators over two regions separated in space and time, we show that the butterfly effect implies scrambling. Finally, we show that these measures of scrambling and chaos do not distinguish between scrambled states of low complexity and generic states of high complexity. This leads us to conjecture that the complexity of the time-evolution operator is holographically dual to the action of the black hole interior.