  Quantum mechanical expectation values for subsets can differ substantially
from those for the whole ensemble. This implies that the effect of interactions
between two systems can be altered substantially by conditioning. Here we
experimentally demonstrate that, for two light fields $\psi_S$ (signal) and
$\psi_A$ (ancilla) that have only weakly interacted with one another,
subsequent measurements on the ancilla can produce substantial conditional
amplification, attenuation, or phase shift of $\psi_S$. We observe conditional
signal power changes within a factor of 30, and phase shift up to $\pi/2$,
induced by small changes in the ancilla measurement basis. The method is
generically applicable to a variety of systems, and allows one to modify or
boost a given interaction by trading in success probability for interaction
strength.
