Wigner negativity is one of the necessary resources for quantum computation with continuous variables. In recent years, this motivated our group to produce a series of works on the measurement-based creation of Wigner-negative states. However, there are a multitude of other important properties that a quantum state can have, such as a high stellar rank, non-linear squeezing, and non-Gaussian entanglement. The aim of the post-doc project is to design new protocols to generate quantum states with non-Gaussian entanglement.