Entanglement measures for intermediate separability of quantum states

We present a family of entanglement measures R_m which act as indicators of separability of n-qubit quantum states into m subsystems for arbitrary 2≤m≤n. The measure R_m vanishes if the state is separable into m subsystems, and for m=n it gives the Meyer-Wallach measure, while for m=2 it reduces, in effect, to the one introduced recently by Love et al. Quantum Inf. Process. 6 187 (2007)]. The measures R_m are evaluated explicitly for the Greenberger-Horne-Zeilinger state and the W state (and its modifications, the W_k or Dicke states) to show that these globally entangled states exhibit rather distinct behaviors under the measures, indicating the utility of the measures R_m for characterizing globally entangled states as well.