An entanglement measure for n qubits

X iv :0 71 0. 34 25 v3 [ qu an tph ] 2 7 Ja n 20 09 An entanglement measure for n qubits Dafa Li, Xiangrong Li, Hongtao Huang, Xinxin Li a Dept of mathematical sciences, Tsinghua University, Beijing 100084 CHINA b Department of Mathematics, University of California, Irvine, CA 92697-3875, USA c Electrical Engineering and Computer Science Department University of Michigan, Ann Arbor, MI 48109, USA d Dept. of Computer Science, Wayne State University, Detroit, MI 48202, USA Pacs: 03.67.Mn, 03.65.Ud. Abstract In Phys. Rev. A 61, 052306 (2000), Coffman, Kundu and Wootters introduced the residual entanglement for three qubits. In this paper, we present the entanglement measure τ(ψ) for even n qubits; for odd n qubits, we propose the residual entanglement τ (ψ) with respect to qubit i and the odd n-tangle R(ψ) by averaging the residual entanglement with respect to each qubit. In this paper, we show that these measures are LU invariant, entanglement monotones, invariant under permutations of the qubits, and multiplicative in some cases.