All the states of $N$ qubits can be classified into $N-1$ entanglement classes from 2-entangled to $N$-entangled (fully entangled) states. Each class of entangled states is characterized by an entanglement index that depends on the partition of $N$. The larger the entanglement index of a state, the more entangled or the less separable is the state in the sense that a larger maximal violation of Bell’s inequality is attainable for this class of state.

• Received 11 November 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.080401