  Quantum dynamics is of fundamental interest and has implications in quantum
information processing. The four-point out-of-time-ordered correlator (OTOC) is
traditionally used to quantify quantum information scrambling under many-body
dynamics. Due to the OTOC's unusual time ordering, its measurement is
challenging. We propose higher-point OTOCs to reveal early-time scrambling
behavior, and present protocols to measure any higher-point OTOC using the
shadow estimation method. The protocols circumvent the need for time-reversal
evolution and ancillary control. They can be implemented in near-term quantum
devices with single-qubit readout.
