Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

We discuss questions in quantum physics that can be cast as non-commutative polynomial optimisation problems and discuss their solution in terms of semi-definite programming. This ranges from new approaches to detect entangled states to the computation of ground state energies of interacting systems. We argue that these methods can play an important role for the certification of quantum effects.