Remote preparation of $W$ states from imperfect bipartite sources

Several proposals to produce {\it tripartite} $W$-type entanglement are probabilistic even if no imperfections are considered in the processes. We provide a deterministic way to remotely create $W$ states out of an EPR source. The proposal is made viable through measurements (which can be demolitive) in an appropriate three-qubit basis. The protocol becomes probabilistic only when source flaws are considered. It turns out that, even in this situation, it is robust against imperfections in two senses: (i) It is possible, after postselection, to create a pure ensemble of $W$ states out of an EPR source containing a systematic error; (ii) If no postselection is done, the resulting mixed state has a fidelity, with respect to a pure $|W\rangle$, which is higher than that of the imperfect source in comparison to an ideal EPR source. This simultaneously amounts to entanglement concentration and {\it lifting}.