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

TL;DR

This paper provides explicit formulas for the three-tangle, a measure of tripartite entanglement, for certain mixed three-qubit states combining generalized GHZ and W states, extending previous methods.

Contribution

It offers a complete solution for the three-tangle of mixed states involving generalized GHZ and W states, including explicit formulas and optimal decompositions.

Findings

Explicit expressions for the three-tangle of mixed states.

Optimal decompositions for the states considered.

General solution for a family of states with GHZ and orthogonal product states.

Abstract

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized 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. 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.