Optical synthesis of large-amplitude squeezed coherent-state superpositions with minimal resources

We propose and experimentally realize a novel versatile protocol that allows the quantum state engineering of heralded optical coherent-state superpositions. This scheme relies on a two-mode squeezed state, linear mixing and a $n$-photon detection. It is optimally using expensive non-Gaussian resources to build up only the key non-Gaussian part of the targeted state. In the experimental case of a two-photon detection based on high-efficiency superconducting nanowire single-photon detectors, the freely propagating state exhibits a 67% fidelity with a squeezed even coherent-state superposition with a size $|\alpha|^2$=3. The demonstrated procedure and the achieved rate will facilitate the use of such superpositions in subsequent protocols, including fundamental tests and optical hybrid quantum information implementations.