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In this article we obtain new results for the task of converting a \textit{single} $N$-qubit W-class state (of the form $\sqrt{x_0}\ket{00...0}+\sqrt{x_1}\ket{10...0}+...+\sqrt{x_N}\ket{00...1}$) 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 \textit{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 $x_0=0$.
- Our proof involves deriving new entanglement monotones defined on the set of four qubit W-class states.
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