Randomly distilling W-class states into general configurations of two-party entanglement

In this article we obtain results for the task of converting a single N-qubit W-class state (of the form √x₀|00...0+√x ₁|10...0++√x_N|00...1) into maximum entanglement shared between two random parties. Previous studies in random distillation have not considered how the particular choice of target pairs affects the transformation, and here we develop a strategy for distilling into general configurations of target pairs. We completely solve the problem of determining the optimal distillation probability for all three-qubit configurations and most four-qubit configurations when x₀=0. Our proof involves deriving new entanglement monotones defined on the set of four-qubit W-class states. As an additional application of our results, we present new upper bounds for converting a generic W-class state into the standard W state |W _N=√1N(|10...0++|00...1).