Heralded Interaction Control between Quantum Systems

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.