Improving entanglement purification through coherent superposition of roles

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 superposed entanglement purification design strategy, leveraging coherent superpositions of the roles of entangled states to enhance purification efficiency, defining a new family of non-Clifford distillation protocols. We demonstrate how this approach can be hierarchically integrated with existing entanglement purification strategies, consistently improving protocols performance.