  The out-of-time order correlator (OTOC) has recently become relevant in
different areas where it has been linked to scrambling of quantum information
and entanglement. It has also been proposed as a good indicator of quantum
complexity. In this sense, the OTOC-RE theorem relates the OTOCs summed over a
complete base of operators to the second Renyi entropy. Here we have studied
the OTOC-RE correspondence on physically meaningful bases like the ones
constructed with the Pauli, reflection, and translation operators. The
evolution is given by a paradigmatic bi-partite system consisting of two
perturbed and coupled Arnold cat maps with different dynamics. We show that the
sum over a small set of relevant operators, is enough in order to obtain a very
good approximation for the entropy and hence to reveal the character of the
dynamics, up to a time t 0 . In turn, this provides with an alternative natural
indicator of complexity, i.e. the scaling of the number of relevant operators
with time. When represented in phase space, each one of these sets reveals the
classical dynamical footprints with different depth according to the chosen
base.
