Nondeterministic amplifier for two-photon superpositions

We examine heralded nondeterministic noiseless amplification based on the quantum scissors device, which has been shown to increase the one-photon amplitude of a state at the expense of the vacuum-state amplitude. Here we propose using the same basic design to perform perfect amplification in a basis set of up to two photons. The device is much more efficient than several one-photon amplifiers working in tandem. When used to amplify coherent states this advantage is shown either using fidelity or in terms of probability of successful action, or more strikingly in a combination of the two.