  A non-trivial $\mathcal{S}$-matrix generally implies a production of
entanglement: starting with an incoming pure state the scattering generally
returns an outgoing state with non-vanishing entanglement entropy. It is then
interesting to ask if there exists a non-trivial $\mathcal{S}$-matrix that
generates no entanglement. In this letter, we argue that the answer is the
scattering of classical black holes. We study the spin-entanglement in the
scattering of arbitrary spinning particles. Augmented with Thomas-Wigner
rotation factors, we derive the entanglement entropy from the gravitational
induced $2\rightarrow 2$ amplitude. In the Eikonal limit, we find that the
relative entanglement entropy, defined here as the \textit{difference} between
the entanglement entropy of the \textit{in} and \textit{out}-states, is nearly
zero for minimal coupling irrespective of the \textit{in}-state, and increases
significantly for any non-vanishing spin multipole moments. This suggests that
minimal couplings of spinning particles, whose classical limit corresponds to
Kerr black hole, has the unique feature of generating near zero entanglement.
