  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.
