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arXiv · 0901.2620

Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?

Eylee Jung·DaeKil Park·Jin-Woo Son
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Abstract

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

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Eylee Jung, DaeKil Park, Jin-Woo Son. 2009-06-19. Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?. https://doi.org/10.1103/physreva.80.010301

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