Heterogeneous multipartite entanglement purification for size-constrained quantum devices

The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elusive. Here we depart from the typical purification paradigm for multipartite states explored in the last 20 years. We present cases where the hardware limitations are taken into account and, surprisingly, find that smaller ``sacrificial'' states, such as Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states. This drastically simplifies the requirements and presents a fundamentally different pathway to leverage near-term networked quantum hardware.