Three-tangle does not properly quantify tripartite entanglement for Greenberger-Horne-Zeilinger-type states

Journal Article · Wed Jul 15 04:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.010301· OSTI ID:21313167

Jung, Eylee; Park, DaeKil; Son, Jin-Woo ^[1]

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1. Department of Physics, Kyungnam University, Masan 631-701 (Korea, Republic of)

Some mixed states composed of only Greenberger-Horne-Zeilinger (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, {pi}{sub GHZ}, is explicitly presented in this Rapid Communication. These results are used to compute analytically the three-tangle of a rank-4 mixed state {sigma} composed of four GHZ states. This analysis with considering Bloch sphere S{sup 16} of d=4 qudit system allows us to derive the hyperpolyhedron. It is shown that the states in this hyperpolyhedron have vanishing three-tangle. Computing the one-tangles for {pi}{sub GHZ} and {sigma}, we prove the monogamy inequality explicitly. Making use of the fact that the three-tangle of {pi}{sub 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.

• OSTI ID: 21313167
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GHZ RANGE
MIXED STATE
QUANTUM COMPUTERS
QUANTUM ENTANGLEMENT
S STATES