Entanglement distillation by extendible maps

It is known that from entangled states that have positive partial transpose it is not possible to distill maximally entangled states by local operations and classical communication (LOCC). A long-standing open question is whether maximally entangled states can be distilled from every state with a non-positive partial transpose. In this paper we study a possible approach to the question consisting of enlarging the class of operations allowed. Namely, instead of LOCC operations we consider k-extendible operations, defined as maps whose Choi-Jamiolkowski state is k-extendible. We find that this class is unexpectedly powerful - e.g. it is capable of distilling EPR pairs even from product states. We also perform numerical studies of distillation of Werner states by those maps, which show that if we raise the extension index k simultaneously with the number of copies of the state, then the class of k-extendible operations is not that powerful anymore and provide a better approximation to the set of LOCC operations.