In this report, we show explicitly that the tangles of an arbitrary pure state in a $2\otimes 2\otimes 4$ system satisfy the monogamy relation. This relation is also generalized to mixed states. As the tangle is always larger than the square of the concurrence, our result implies that the monogamy relation holds for concurrence too. It also supports the idea that the tangle could qualify as an elementary bipartite entanglement measure.

• Received 15 November 2009

DOI:https://doi.org/10.1103/PhysRevA.81.024305