Bounds on quantum nonlocality

One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an intermediate step, the development of efficiently computable bounds has played an important role for the advance of the field. In this thesis we phrase the problem of determining the quantum value of a Bell expression in the framework of computational complexity. Then we present our contributions exploring efficiently computable bounds (based on the spectral norm of some matrices) to the quantum value of a particular class of Bell inequalities: the linear games. We derive several results for the bipartite and the multipartite scenarios.