  We define a property called nondegeneracy for Bell inequalities, which
describes the situation that in a Bell setting, if a Bell inequality and
involved local measurements are chosen and fixed, any quantum state with a
given dimension and its orthogonal quantum state cannot violate the inequality
remarkably at the same time. By choosing a proper nondegenerate Bell
inequality, we prove that for a unknown bipartite quantum state of a given
dimension, based on the measurement statistics only, we can provide an analytic
lower bound for the entanglement of formation or even for the distillable
entanglement, making the whole process semi-device-independent. We characterize
the mathematical structure of nondegenerate Bell inequalities, and prove that
quite a lot of well-known Bell inequalities are nondegenerate. We demonstrate
our approach by quantifying entanglement for qutrit-qutrit states based on
their violation to the CGLMP inequality.
