  We present a method to calculate an upper bound on the generation of
entanglement in any spin system using the Fannes-Audenaert inequality for the
von Neumann entropy. Our method not only is useful for efficiently estimating
entanglement, but also shows that entanglement generation depends on the
distance of the quantum states of the system from corresponding
minimum-uncertainty spin coherent states (SCSs). We illustrate our method using
a quantum kicked top model, and show that our upper bound is a very good
estimator for entanglement generated in both regular and chaotic regions. In a
deep quantum regime, the upper bound on entanglement can be high in both
regular and chaotic regions, while in the semiclassical regime, the bound is
higher in chaotic regions where the quantum states diverge from the
corresponding SCSs. Our analysis thus explains previous studies and clarifies
the relationship between chaos and entanglement.
