  We introduce a hierarchy of conditions necessarily satisfied by any
distribution P(ab) representing the probabilities for two separate observers to
obtain outcomes a and b when making local measurements on a shared quantum
state. Each condition in this hierarchy is formulated as a semidefinite
program. Our approach can be used to obtain upper-bounds on the quantum
violation of an arbitrary Bell inequality. It yields, for instance, tight
bounds for the violations of the Collins et al. inequalities.
