  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.
