  While all bipartite pure entangled states are known to generate correlations
violating a Bell inequality, and are therefore nonlocal, the quantitative
relation between pure-state entanglement and nonlocality is poorly understood.
In fact, some Bell inequalities are maximally violated by non-maximally
entangled states and this phenomenon is also observed for other operational
measures of nonlocality. In this work, we study a recently proposed measure of
nonlocality defined as the probability that a pure state displays nonlocal
correlations when subjected to random measurements. We first prove that this
measure satisfies some natural properties for an operational measure of
nonlocality. Then, we show that for pure states of two qubits the measure is
monotonic with entanglement for all correlation two-outcome Bell inequalities:
for all these inequalities, the more the state is entangled, the larger the
probability to violate them when random measurements are performed. Finally, we
extend our results to the multipartite setting.
