  If black holes were able to clone quantum states, a number of paradoxes in
black hole physics would disappear. However, the linearity of quantum mechanics
forbids exact cloning of quantum states. Here we show that black holes indeed
clone incoming quantum states with a fidelity that depends on the black hole's
absorption coefficient, without violating the no-cloning theorem because the
clones are only approximate. Perfectly reflecting black holes are optimal
universal "quantum cloning machines" and operate on the principle of stimulated
emission, exactly as their quantum optical counterparts. In the limit of
perfect absorption, the fidelity of clones is equal to what can be obtained via
quantum state estimation methods. But for any absorption probability less than
one, the cloning fidelity is nearly optimal as long as $\omega/T\geq10$, a
common parameter for modest-sized black holes.
