Non-Gaussian state preparation and enhancement using weak-value amplification

We introduce a protocol for generating non-Gaussian (nG) states via postselected weak measurement. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports of an interferometer with a third-order nonlinear medium. An nG state is conditionally produced at the signal output, heralded by single-photon detection in an idler output channel. The protocol exploits a weak cross-Kerr interaction, with effective single-photon nonlinearity enhanced by weak-value amplification. By tuning the weak value of the idler photon number operator within experimentally feasible parameters, diverse nG states can be generated with high fidelity. Specific examples include photon-added coherent states, displaced and squeezed number states, and intermediate nG states from coherent and squeezed vacuum inputs. Furthermore, the protocol enables enhancement of non-Gaussianity and enlargement of Schrödinger cat (SC) states when ideal SC states are used as input. Our results provide an alternative route for conditional generation of tunable nG states, with potential applications in quantum information processing and state engineering.