Multiple Entropy Measures for Multipartite Quantum Entanglement

A new entanglement measure, the multiple entropy measures (MEMS), is proposed to quantify quantum entanglement of multi-partite quantum state. The MEMS is vector-like with $m=[N/2]$, the integer part of $N/2$, components: $[S_1, S_2,..., S_m]$, and the $i$-th component $S_i$ is the geometric mean of $i$-body partial entropy of the system. The $S_i$ measures how strong an arbitrary $i$ bodies from the system are entangled with the rest of the system. The MEMS is not only transparent in physical picture, but also simple to calculate. It satisfies the conditions for a good entanglement measure. We have analyzed the entanglement properties of the GHZ-state, the W-states and cluster-states under MEMS. The cluster-state is more entangled than the GHZ-state and W-state under MEMS.