Three-tangle for mixtures of generalized GHZ and generalized W states

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized Greenberger–Horne–Zeilinger (GHZ) state, a|000+b|111, and a generalized W state, c|001+d|010+f|100. Using the methods introduced by Lohmayer et al (2006 Phys. Rev. Lett. 97 260502), we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case, we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state.

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