  Einstein's theory of gravity admits a low energy effective quantum field
description from which predictions beyond classical general relativity can be
drawn. As gravitational wave detectors improve, one may ask whether
non-classical features of such theory can be experimentally verified. Here we
argue that nonlinear effects in black hole ringdowns can be sensitive to the
graviton number statistics and other quantum properties of gravitational wave
states. The prediction of ringdown signals, potentially measurable in the near
future, might require the inclusion of quantum effects. This offers a new route
to probing the quantum nature of gravity and gravitational wave entanglement.
