Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states - Quantum PhysicsReport as inadecuate




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Abstract: Some mixed states composed of only GHZ states can be expressed in terms ofonly W-states. This fact implies that such states have vanishing three-tangle.One of such rank-3 states, $\Pi {GHZ}$, is explicitly presented in this paper.These results are used to compute analytically the three-tangle of a rank-4mixed state $\sigma$ composed of four GHZ states. This analysis withconsidering Bloch sphere $S^{16}$ of $d=4$ qudit system allows us to derive thehyper-polyhedron. It is shown that the states in this hyper-polyhedron havevanishing three-tangle. Computing the one-tangles for $\Pi {GHZ}$ and $\sigma$,we prove the monogamy inequality explicitly. Making use of the fact that thethree-tangle of $\Pi {GHZ}$ is zero, we try to explain why the W-class in thewhole mixed states is not of measure zero contrary to the case of pure states.



Author: Eylee Jung, DaeKil Park, Jin-Woo Son

Source: https://arxiv.org/







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