Multipartite quantum resource distillation through local measurement programs

Abstract: Distributed quantum resources in practical multi-user quantum networks are inevitably degraded by environmental noise, channel loss, and device-induced imperfections. To address these issues, quantum resource distillation offers a fundamental approach to recovering stronger resources from imperfect states. However, conventional implementations often require additional copies, dedicated physical filtering elements, or restrict to bipartite systems, posing challenges for scalable multipartite networks. Here, we introduce the method of quantum resource distillation based on the local measurement program (LMP), which transfers completely positive maps into programmable measurement processes. We experimentally demonstrate the performance of resource distillation through LMP in both bipartite and tripartite photonic systems, including the activation and enhancement of multipartite steering configurations. To demonstrate the flexibility and extensibility of the LMP framework, we also show that virtual resource distillation can be naturally reformulated within it. Our results establish a programmable and experimentally economical approach for distilling quantum resources in multipartite and higher-dimensional systems, thereby providing a practical route toward scalable quantum networks.