  The advent of quantum technologies brought forward much attention to the
theoretical characterization of the computational resources they provide. A
method to quantify quantum resources is to use a class of functions called
magic monotones and stabilizer entropies, which are, however, notoriously hard
and impractical to evaluate for large system sizes. In recent studies, a
fundamental connection between information scrambling, the magic monotone mana
and 2-Renyi stabilizer entropy was established. This connection simplified
magic monotone calculation, but this class of methods still suffers from
exponential scaling with respect to the number of qubits. In this work, we
establish a way to sample an out-of-time-order correlator that approximates
magic monotones and 2-Renyi stabilizer entropy. We numerically show the
relation of these sampled correlators to different non-stabilizerness measures
for both qubit and qutrit systems and provide an analytical relation to 2-Renyi
stabilizer entropy. Furthermore, we put forward and simulate a protocol to
measure the monotonic behaviour of magic for the time evolution of local
Hamiltonians.
