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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 andoperations. Here, we show that the Einstein-Podolsky-Rosen steering inequalitycan be used to obtain a practical witness for the generation of pure bipartitenon-Gaussian states. While the scenario require pure states, we show its broadrelevance by reporting the experimental observation of the non-Gaussianity ofthe CV two-photon state generated in the process of spontaneous parametricdown-conversion (SPDC). The observed non-Gaussianity is due only to theintrinsic phase-matching conditions of SPDC

Non-Gaussian state generation certified using the EPR-steering inequality