Probabilistic amplification and cloning of phase-covariant coherent states

The authors present a novel probabilistic cloner for a phase covariant alphabet. Unlike other approaches, our scheme does neither require high interferometric stability nor non-classical resources such as single photons, but it is based solely on a random displacement and photon counting. The input state is amplified and subsequently split symmetrically to obtain the clones. The amplification is done in two steps. First the coherent state is displaced in phase space with a fixed amplitude but random phase as illustrated in the paper. Subsequently a small portion of the displaced state is tapped off and sent to a photon number resolving detector PNRD. The tapped-off and transmitted part of the state are classically correlated due to the random displacements, which forms the basis of the heralding process. Successful amplification is heralded if the number of clicks in the PNRD equals or surpasses a certain threshold parameter. The highest probability to detect photons in the tap measurement is given if the state is displaced along the original direction of excitation, such that these states are preferred by the heralding process and the mean amplitude of the state is increased. With a rising photon number threshold the residual noise is reduced and the output is more and more approaching a pure state.