  We consider an infinite-range interacting quantum spin-1/2 model, undergoing
periodic kicking and dissipatively coupled with an environment. In the
thermodynamic limit, it is described by classical mean-field equations that can
show regular and chaotic regimes. At finite size, we describe the system
dynamics using stochastic quantum trajectories. We find that the asymptotic
nonstabilizerness (alias the magic, a measure of quantum complexity), averaged
over trajectories, mirrors the classical chaotic behavior, while the
entanglement entropy has no relation with chaos in the thermodynamic limit.
