  Quantum state merging is one of the most important protocols in quantum
information theory. In this task two parties aim to merge their parts of a pure
tripartite state by making use of additional singlets while preserving
correlations with a third party. We study a variation of this scenario where
the shared state is not necessarily pure, and the merging parties have free
access to local operations, classical communication, and PPT entangled states.
We provide general conditions for a state to admit perfect merging, and present
a family of fully separable states which cannot be perfectly merged if the
merging parties have no access to additional singlets. We also show that free
PPT entangled states do not give any advantage for merging of pure states, and
the conditional entropy plays the same role as in standard quantum state
merging quantifying the rate of additional singlets needed to perfectly merge
the state.
