Correlated entanglement distillation and the structure of the set of undistillable states

Understand

We consider entanglement distillation under the assumption that the input states are allowed to be correlated among each other.

• We hence replace the usually considered independent and identically-distributed hypothesis by the weaker assumption of merely having identical reductions.
• We find that whether a state is then distillable or not is only a property of these reductions, and not of the correlations that are present in the input state.
• This is shown by establishing an appealing relation between the set of copy-correlated undistillable states and the standard set of undistillable states: The former turns out to be the convex hull of the latter.