  We show that weak measurement can be used to "amplify" optical nonlinearities
at the single- photon level, such that the effect of one properly post-selected
photon on a classical beam may be as large as that of many un-post-selected
photons. We find that "weak-value amplification" offers a marked improvement in
signal-to-noise ratio in the presence of technical noise with long correlation
times. Unlike previous weak measurement experiments, our proposed scheme has no
classical equivalent.
