Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof

Understand

New measures of multipartite entanglement are constructed based on two definitions of multipartite information and different methods of optimizing over extensions of the states.

• One is a generalization of the squashed entanglement where one takes the mutual information of parties conditioned on the state's extension and takes the infimum over such extensions.
• Additivity of the multipartite squashed entanglement is proved for both versions of the multipartite information which turn out to be related.
• The second one is based on taking classical extensions.