Relationship between the n-tangle and the residual entanglement of even n qubits

Details Relationship between the n-tangle and the residual entanglement of even n qubits Relationship between the n-tangle and the residual entanglement of even n qubits

2010-03-24

arxiv.org/abs/1003.4774v1

Quantum Inf. Comput. 10, 1018 (2010)

Physics

Quantum Physics

8 pages, no figures

Scientific paper

We show that $n$-tangle, the generalization of the 3-tangle to even $n$ qubits, 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.

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