Is there a non-deterministic protocol for entanglement generation between distant parties?

Question

I'm aware that one can imperfectly clone entanglement that's shared between two parties (i.e. Bell pairs) using deterministic quantum cloning machines to produce two, lower fidelity entangled states.

What I want to know is, does there exist some strategy to non-deterministically generate entanglement between two distant parties? In other words if Alice and Bob have a Bell pair between them, is there some LOCC strategy they can do that will either create another Bell pair of the same fidelity, or fail wiith some probability.

Answer 1

No. By definition, the set of states that you can produce under LOCC are the separable states. This includes all possible measurements, post-selection on certain outcomes etc. The whole point of entanglement is that it's the stuff that cannot be made via LOCC. Hence, if you have it, it's a resource that is useful to people who are operating under LOCC restrictions.

Answer 2

No, any such protocol would violate the holevo bound (1 bit of communication per 1 sent qubit, including qubits sent during preparation). You could just keep repeating the process until it gave you entanglement, then use superdense coding to achieve 2 bits per qubit.