Practical Framework for Conditional Non-Gaussian Quantum State Preparation

We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian state. We apply this formalism to several examples, thus showing its potential as an elegant analytical tool for simulating quantum optics experiments. Furthermore, we also use it to prove that Einstein-Podolsky-Rosen steering is a necessary requirement to remotely prepare a Wigner-negative state.