The n-tangle of odd n qubits

Coffman, Kundu and Wootters presented the 3-tangle of three qubits in [Phys. Rev. A 61, 052306 (2000)]. Wong and Christensen extended the 3-tangle to even number of qubits, known as $n$-tangle [Phys. Rev. A 63, 044301 (2001)]. In this paper, we propose a generalization of the 3-tangle to any odd $n$-qubit pure states and call it the $n$-tangle of odd $n$ qubits. We show that the $n$-tangle of odd $n$ qubits is invariant under permutations of the qubits, and is an entanglement monotone. The $n$-tangle of odd $n$ qubits can be considered as a natural entanglement measure of any odd $n$-qubit pure states.