Bell inequality, separability and entanglement distillation

In this review, we introduce well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states. It is shown that any pure entangled quantum state violates one of Bell-like inequalities. Moreover, quantum states that violate any one of these Bell-like inequalities are shown to be distillable. New Bell inequalities that detect more entangled mixed states are also introduced.