Potential multiparticle entanglement measure

In this Brief Report we discuss entanglement of multiparticle quantum systems. We propose a potential measure of a type of entanglement of pure states of n qubits, the n-tangle. For a system of two qubits the n-tangle is equal to the square of the concurrence, and for systems of three qubits it is equal to the “residual entanglement.” We show that the n-tangle is also equal to a generalization of the concurrence squared for even n, and use this fact to prove that the n-tangle is an entanglement monotone. However, the n-tangle is undefined for odd n>3. Finally, we propose a measure related to the n-tangle for mixed-state systems of n qubits, and find an analytical formula for this measure for even n.