Non-Gaussian-state generation certified using the Einstein-Podolsky-Rosen-steering inequality

Due to practical reasons, experimental and theoretical continuous-variable (CV) quantum information (QI) has been heavily based on Gaussian states. Nevertheless, many CV-QI protocols require the use of non-Gaussian states and operations. Here, we show that the Einstein-Podolsky-Rosen-steering inequality can be used to obtain a practical witness for the generation of pure bipartite non-Gaussian states. While the scenario requires pure states, we show its broad relevance by reporting the experimental observation of the non-Gaussianity of the CV two-photon state generated in the process of spontaneous parametric down-conversion (SPDC). The observed non-Gaussianity is due only to the intrinsic phase-matching conditions of SPDC.