Black holes are almost optimal quantum cloners

Abstract

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 $ω/T\geq10$, a common parameter for modest-sized black holes.