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Entanglement and Bell nonlocality are used to describe quantuminseparabilities. Bell-nonlocal states form a strict subset of entangledstates. A natural question arises concerning how much territory Bellnonlocality occupies entanglement for a general two-qubit entangled state. Inthis work, we investigate the relation between entanglement and Bellnonlocality by using lots of randomly generated two-qubit states, and give outa constraint inequality relation between the two quantum resources. Forstudying the upper or lower boundary of the inequality relation, we discovermaximally (minimally) nonlocal entangled states, which maximize (minimize) thevalue of the Bell nonlocality for a given value of the entanglement.Futhermore, we consider a special kind of mixed state transformed by performingan arbitrary unitary operation on werner state. It is found that the specialmixed state's entanglement and Bell nonlocality are related to ones of a purestate transformed by the unitary operation performed on the Bell state.

Inequality relation between entanglement and Bell nonlocality for arbitrary two-qubit states