Certification of Non-Gaussian States using Double Homodyne Detection

Certifying reliable sources for quantum information processing is still one of the major challenges towards practical applications. Continuous variable quantum information provides a very promising platform where important resources such as scalable entanglement come "for free" [1] . In that context, a crucial quantum feature to look for and investigate is the so-called non-Gaussianity, which, beyond its conceptual relevance, is a necessary resource for any quantum computational advantage as well as for effective error correction, entanglement distillation and more. Non-Gaussian states have been produced and probed using full tomography techniques [2] . However, performing a full tomography of multimode continuous variable systems is a hard problem. Indeed, systems aimed at overcoming classical approach are by definition too complex to be fully characterized, thus alternative approaches are required.