Multiple Entropy Measures for Multi-particle Pure Quantum Statet

We propose to use a set of averaged entropies, the multiple entropy measures （MEMS）, to partially quantify quantum entanglement of multipartite quantum state. The MEMS is vector-like with m = [N/2] components： [S1, S2,..., Sm], and the i-th component Si is the geometric mean of i-qubits partial entropy of the system. The Si measures how strong an arbitrary i qubits from the system are correlated with the rest of the system. 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.