  Nonlocality and entanglement are not only the fundamental characteristics of
quantum mechanics but also important resources for quantum information and
computation applications. Exploiting the quantitative relationship between the
two different resources is of both theoretical and practical significance. The
common choice for quantifying the nonlocality of a two-qubit state is the
maximal violation of the Clauser-Horne-Shimony-Holt inequality. That for
entanglement is entanglement of formation, which is a function of the
concurrence. In this paper, we systematically investigate the quantitative
relationship between the entanglement and nonlocality of a general two-qubit
system. We rederive a known upper bound on the nonlocality of a general
two-qubit state, which depends on the state's entanglement. We investigate the
condition that the nonlocality of two different two-qubit states can be
optimally stimulated by the same nonlocality test setting and find the class of
two-qubit state pairs that have this property. Finally, we obtain the necessary
and sufficient condition that the upper bound can be reached.

Quantum Physics