  Let us consider the set of joint quantum correlations arising from
two-outcome local measurements on a bipartite quantum system. We prove that no
finite dimension is sufficient to generate all these sets. We approach the
problem in two different ways by constructing explicit examples for every
dimension d, which demonstrates that there exist bipartite correlations that
necessitate d-dimensional local quantum systems in order to generate them. We
also show that at least 10 two-outcome measurements must be carried out by the
two parties altogether so as to generate bipartite joint correlations not
achievable by two-dimensional local systems. The smallest explicit example we
found involves 11 settings.
