Obtaining a single-photon weak value from experiments using a strong (many-photon) coherent state

A common type of weak-value experiment prepares a single particle in one state, weakly measures the occupation number of another state, and post-selects on finding the particle in a third state (a "click"). Most weak-value experiments have been done with photons, but the heralded preparation of a single photon is difficult and slow of rate. Here, we show that the weak value mentioned above can be measured using strong (many-photon) coherent states, while still needing only a click detector such as an avalanche photodiode. One simply subtracts the no-click weak value from the click weak-value and scales the answer by a simple function of the click probability.