  The out-of-time order correlator (OTOC) has been widely studied in closed
quantum systems. However, there are very few studies for open systems and they
are mainly focused on isolating the effects of scrambling from those of
decoherence. Adopting a different point of view, we study the interplay between
these two processes. This proves crucial in order to explain the OTOC behavior
when a phase space contracting dissipation is present, ubiquitous not only in
real life quantum devices but in the dynamical systems area. The OTOC decay
rate is closely related to the classical Lyapunov exponent -- with some
differences -- and more sensitive in order to distinguish the chaotic from the
regular behavior than other measures. On the other hand, it reveals as a
generally simple function of the longest lived eigenvalues of the quantum
evolution operator. We find no simple connection with the Ruelle-Pollicott
resonances, but by adding Gaussian noise of $\hbar_{\text{eff}}$ size to the
classical system we recover the OTOC decay rate, being this a consequence of
the correspondence principle put forward in [Physical Review Letters 108 210605
(2012) and Physical Review E 99 042214 (2019)]
