Optimal architecture for a nondeterministic noiseless linear amplifier

Nondeterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the performance of quantum key distribution, purifying lossy channels, and distilling entanglement. Previous designs for noiseless linear amplifiers involving linear optics and photon counting are nonoptimal because they have a probability of success lower than the bound given by the theory of generalized quantum measurement. This paper develops a theoretical model using unitary interactions and projective measurements which reaches this limit. We calculate the fidelity and probability of success of this model for coherent states and Einstein-Podolsky-Rosen entangled states. Finally, we explore some examples of the complex interplay between the fidelity, probability, and the distilling and purifying power of the model.