Global entangling properties of the coupled kicked tops.

We study global entangling properties of the system of coupled kicked tops testing various hypotheses and predictions concerning entanglement in quantum chaotic systems. In order to analyze the averaged initial entanglement production rate and the averaged asymptotic entanglement, various ensembles of initial product states are evolved. Two different ensembles with natural probability distribution are considered: product states of independent spin-coherent states and product states of random states. It appears that the choice of either of these ensembles results in significantly different averaged entanglement behavior. We investigate also a relation between the averaged asymptotic entanglement and the mean entanglement of eigenvectors of the evolution operator. Lower bound on the averaged asymptotic entanglement is derived, expressed in terms of the eigenvector entanglement.