  Out-of-time-ordered correlators (OTOCs) have been proposed as a tool to
witness quantum information scrambling in many-body system dynamics. These
correlators can be understood as averages over nonclassical multi-time
quasi-probability distributions (QPDs). These QPDs have more information, and
their nonclassical features witness quantum information scrambling in a more
nuanced way. However, their high dimensionality and nonclassicality make QPDs
challenging to measure experimentally. We focus on the topical case of a
many-qubit system and show how to obtain such a QPD in the laboratory using
circuits with three and four sequential measurements. Averaging distinct values
over the same measured distribution reveals either the OTOC or parameters of
its QPD. Stronger measurements minimize experimental resources despite
increased dynamical disturbance.
