  There is a remarkable interest in the study of Out-of-time ordered
correlators (OTOCs) that goes from many body theory and high energy physics to
quantum chaos. In this latter case there is a special focus on the comparison
with the traditional measures of quantum complexity such as the spectral
statistics, for example. The exponential growth has been verified for many
paradigmatic maps and systems. But less is known for multi-partite cases. On
the other hand the recently introduced Wigner separability entropy (WSE) and
its classical counterpart (CSE) provide with a complexity measure that treats
equally quantum and classical distributions in phase space. We have compared
the behavior of these measures in a system consisting of two coupled and
perturbed cat maps with different dynamics: double hyperbolic (HH), double
elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and
the WSE have essentially the same behavior, providing with a complete
characterization in generic bi-partite systems and at the same time revealing
them as very good measures of quantum complexity for phase space distributions.
Moreover, we establish a relation between both quantities by means of a
recently proven theorem linking the second Renyi entropy and OTOCs.
