Randomly distilling W -class states into general configurations of two-party entanglement
Wei Cui, Eric Chitambar, Hoi‐Kwong Lo · Physical Review A · 2011
In this article we obtain results for the task of converting a single $N$-qubit $W$-class state (of the form $\sqrt{{x}_{0}}|00...0\ensuremath{\rangle}+\sqrt{{x}_{1}}|10...0\ensuremath{\rangle}+\ensuremath{\cdots}+\sqrt{{x}_{N}}|00...1\ensuremath{\rangle}$) 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 ${x}_{0}=0$. 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 $|{W}_{N}\ensuremath{\rangle}=\sqrt{\frac{1}{N}}(|10...0\ensuremath{\rangle}+\ensuremath{\cdots}+|00...1\ensuremath{\rangle})$.