Bipartite probabilistic correlations can be used to describe quantum behaviour in finite-input, finite-output systems involving two parties (Alice and Bob). In recent years, there has been a lot of progress in separating the correlation sets corresponding to different models of quantum mechanics. In this talk, we’ll consider a matrix-valued generalization of these correlations, which can be thought of as partial measurements on Alice and Bob’s system. We will see how we can separate certain models using matrix-valued correlations in situations where the analogous separations for probabilistic correlation sets are not known. This is based on joint work with Li Gao and Marius Junge.