  Quantum networks hold the promise for revolutionary advances in information
processing with quantum resources distributed over remote locations via
quantum-repeater architectures. Quantum networks are composed of nodes for
storing and processing quantum states, and of channels for transmitting states
between them. The scalability of such networks relies critically on the ability
to perform conditional operations on states stored in separated quantum
memories. Here we report the first implementation of such conditional control
of two atomic memories, located in distinct apparatuses, which results in a
28-fold increase of the probability of simultaneously obtaining a pair of
single photons, relative to the case without conditional control. As a first
application, we demonstrate a high degree of indistinguishability for remotely
generated single photons by the observation of destructive interference of
their wavepackets. Our results demonstrate experimentally a basic principle for
enabling scalable quantum networks, with applications as well to linear optics
quantum computation.
