Entanglement theory where you do not expect it: multipartite violation of Gleason's theorem and stochastic simulation of channels in quantum optics

Entanglement theory is an important part of quantum information that aims to characterize, quantify and exploit entanglement. Concepts and tools from entanglement theory can find applications in unexpected ways. I will provide evidence for this by presenting two recent results that range from a foundational issue to the simulation of quantum channels in quantum optics. The first one regards what can be considered a violation of Gleason's theorem in the multipartite setting. Roughly speaking, the validity of quantum mechanics at a local level and the non-signalling condition do not imply quantum correlations: counterexamples can be found that are related to multipartite bound entanglement. The second result is a scheme to simulate perfectly but stochastically any quantum channel on a d-rail qudit. We find that the probability of success depends on the entanglement properties of the Choi-Jamiołkowski state isomorphic to the channel.