  We discuss the recently introduced concept of non-deterministic noiseless
linear amplification, demonstrating that such an operation can only be
performed perfectly with vanishing probability of success. We show that a weak
measurement, which imprints the weak value of an observable of a pre-selected
and post-selected system onto a probe system, can be used to approximate
probabilistic noiseless amplification. This result may be applied to various
tasks in continuous variable quantum information, including entanglement
concentration, probabilistic cloning, and in quantum repeaters. We discuss the
application of our scheme to probabilistic cloning of weak coherent states.
