  Entanglement purification and distillation protocols are essential for
harnessing the full potential of quantum communication technologies. Multiple
strategies have been proposed to approach and optimize such protocols, most
however restricted to Clifford operations. In this paper, we introduce a novel
superposed entanglement purification design strategy, leveraging coherent
superpositions of the roles of entangled states to enhance purification
efficiency. We demonstrate how this approach can be hierarchically integrated
with existing entanglement purification strategies, consistently improving
protocols performance.
