An all-optical transistor is a device in which a gate light pulse switches
the transmission of a target light pulse with a gain above unity. The gain
quantifies the change of the transmitted target photon number per incoming gate
photon. We study the quantum limit of one incoming gate photon and observe a
gain of 20. The gate pulse is stored as a Rydberg excitation in an ultracold
gas. The transmission of the subsequent target pulse is suppressed by Rydberg
blockade which is enhanced by a F\"orster resonance. The detected target
photons reveal in a single shot with a fidelity above 0.86 whether a Rydberg
excitation was created during the gate pulse. The gain offers the possibility
to distribute the transistor output to the inputs of many transistors, thus
making complex computational tasks possible
