  In ergodic many-body quantum systems, locally encoded quantum information
becomes, in the course of time evolution, inaccessible to local measurements.
This concept of "scrambling" is currently of intense research interest,
entailing a deep understanding of many-body dynamics such as the processes of
chaos and thermalization. Here, we present first experimental demonstrations of
quantum information scrambling on a 10-qubit trapped-ion quantum simulator
representing a tunable long-range interacting spin system, by estimating
out-of-time ordered correlators (OTOCs) through randomized measurements. We
also analyze the role of decoherence in our system by comparing our
measurements to numerical simulations and by measuring R\'enyi entanglement
entropies.
