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 vertical bar 000 > + b vertical bar 111 >, and a generalized W state, c vertical bar 001 > + d vertical bar 010 > + f vertical bar 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. DFG/SFB/631 DFG/Heisenberg Programme