The emergence of the arrow of time in quantum many-body systems stems from the inherent tendency of Hamiltonian evolution to scramble quantum information and increase entanglement. While, in principle, one might counteract this temporal directionality by engineering a perfectly inverted Hamiltonian to reverse entanglement growth, such a scenario is fundamentally unstable because even minor imperfections in the backward evolution can be exponentially amplified, a hallmark of quantum many-body chaos. Therefore, successfully reversing quantum many-body dynamics demands a deep understanding of the underlying structure of quantum information scrambling and chaotic dynamics. In this Letter, by using solid-state nuclear magnetic resonance on a macroscopic ensemble of randomly interacting spins, we measure the out-of-time-ordered correlator and validate key predictions of scramblon theory, a universal theoretical framework for information scrambling. Crucially, this theory enables us to isolate and mitigate errors in the out-of-time-ordered correlator caused by imperfections in the backward evolution. As a result, this protocol uncovers the anticipated exponential behavior of quantum many-body chaos and extracts the quantum Lyapunov exponent in a many-body experimental system for the first time. Our results push the fundamental limits of dynamical reversibility of complex quantum systems, with implications for quantum simulation and metrology.

Close

PrevNext

View figure in article

• Information scrambling
• Quantum chaos
• Quantum simulation