The Interplay of Quantum Information Scrambling and Chaos

Quantum chaos and information scrambling are understood as highly generic phenomena in large systems. These concepts underlie a range of fundamental questions, such as: the simulatability of dynamics on classical or quantum computers; the emergence of statistical physics and thermodynamics from isolated quantum theory; and determining the mechanisms behind the black hole information paradox.

Scrambling, as measured by out-of-time-order correlators (OTOCs), quantify the spread of quantum information. Recent results hint that information scrambling should be distinguished as a different notion from quantum chaos. However, the exact relationship remains a pressing question. Our work addresses this issue by presenting a novel relationship between the general OTOC and quantum chaos. In particular, we show that scrambling is strictly necessary for chaos.

We utilize tools from quantum information theory to achieve this, to upper bound the OTOC by the local-operator entanglement (LOE), a dynamical signature of chaos. In doing so, we will uncover simple cases where a dynamics is scrambling as signified by an exponential OTOC scaling, yet is not chaotic as demonstrated by a slow LOE entropy growth. We do this through exact analytical computations for a class of many-body local circuits called dual unitaries, including both integrable and chaotic examples. Our results lay bare the relationship between scrambling and chaos, providing insight into the emergent phenomena of many-body quantum systems.