Relationship between the n-tangle and the residual entanglement of even n qubits
Xiangrong Li, Dafa Li · Quantum Information and Computation · 2010
We show that for even $n$ qubits,$\ n$-tangle is the square of the SLOCC polynomial invariant of degree 2. We find that the $n$-tangle is not the residual entanglement for any even $n\geq 4$\ qubits. We give a necessary and sufficient condition for the vanishing of the concurrence $C_{1(2...n)}$. The condition implies that the concurrence $C_{1(2...n)}$ is always positive for any entangled states while the $n$-tangle vanishes for some entangled states. We argue that for even $n$\ qubits, the concurrence $ C_{1(2...n)}$\ is equal to or greater than the $n$-tangle.\ Further, we reveal that the residual entanglement is a partial measure for product states of any $n$ qubits while the $n$-tangle is multiplicative for some product states.