  Nonlocality is one of the most important resources for quantum information
protocols. The observation of nonlocal correlations in a Bell experiment is the
result of appropriately chosen measurements and quantum states. We quantify the
minimal purity to achieve a certain Bell value for any Bell operator. Since
purity is the most fundamental resource of a quantum state, this enables us
also to quantify the necessary coherence, discord, and entanglement for a given
violation of two-qubit correlation inequalities. Our results shine new light on
the CHSH inequality by showing that for a fixed Bell violation an increase in
the measurement resources does not always lead to a decrease of the minimal
state resources.
