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

Abstract

In this article we obtain new results for the task of converting a \textit{single} $N$-qubit W-class state (of the form $\sqrt{x_0}|\mathrm{00...0}⟩+\sqrt{x_1}|\mathrm{10...0}⟩+...+\sqrt{x_N}|\mathrm{00...1}⟩$) 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. As an additional application of our results, we present new upper bounds for converting a generic W-class state into the standard W state $|W_N⟩=\sqrt{\frac{1}{N}}(|\mathrm{10...0}⟩+...+|\mathrm{00...1}⟩)$.