Unambigous preparation of Bell pairs

The preparation of Bell pairs, i.e., entanglement concentration and distillation methods have been intensively studied in the past decades. Although these schemes have since been further optimized, they have remained rather impractical for current physical implementations. We present a practical, iterative LOCC protocol which is able to transform any unknown two-qubit pure input state into a perfect |Φ₊〉 Bell state in two iterations if the input state contains some initial entanglement, and is accessible in many copies. Separable input states never produce outputs after the second iteration, thus, if a successful output is realized, the parties can be sure that the |Φ₊〉 Bell state was produced. There is a zero measure set of input states for which the second iteration does not succeed even though they are entangled. We devise a method to distinguish these states from separable inputs and to rotate them by local operations so that they can also be transformed to a |Φ₊〉 Bell pair. We also show that three iterations of the protocol distill into an approximate |Φ₊〉 Bell pair with quadratically suppressed noise provided that the noise is small, but irrespective of its form.