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

Abstract: We introduce a protocol for generating a broad class of non-Gaussian (nG) quantum states via postselected weak measurement techniques. The scheme involves injecting an arbitrary quantum state and a single photon into the signal and idler ports, respectively, of an interference setup that incorporates a third-order nonlinear medium. A nG state is conditionally produced at the signal output, heralded by the detection of a single photon in one of the idler output channels. The protocol exploits a weak cross-Kerr interaction and effective single-photon nonlinearity enhanced by the weak-value amplification. We show that by tuning the weak value of the photon number operator in the idler mode within experimentally feasible parameters, a wide variety of nG states can be generated with high fidelity. As specific examples, we demonstrate the generation of photon-added states, displaced and squeezed number states, and a continuum of intermediate nG states using coherent and squeezed vacuum inputs, respectively. Furthermore, we show that the protocol enables the enhancement of non-Gaussianity and the enlargement of Schr\"odinger cat (SC) states when ideal SC states are used as the input. Our results provide an alternative route for the conditional generation of tunable nG states, with potential applications in quantum information processing. This approach may also open new avenues for quantum state engineering using postselected weak measurements.