Shortcut to multipartite entanglement generation: A graph approach to boson subtractions

We propose a graph method for systematically searching for schemes that can generate multipartite entanglement in linear bosonic systems with heralding. While heralded entanglement generation offers more tolerable schemes for quantum tasks than postselected ones, it is generally more challenging to find appropriate circuits for multipartite systems. We show that our graph mapping from boson subtractions provides handy tactics to overcome the limitations in circuit designs. Within our graph framework, we identify enhanced schemes for qubit N-partite GHZ, W, and the superposition of N = 3 GHZ and W states. Furthermore, we have found a qudit N-partite GHZ state generation scheme, which requires substantially fewer particles than previous proposals. These results demonstrate the power of our approach in discovering optimized solutions for the generation of intricate heralded entangled states. We expect our method to serve as a promising tool in generating diverse entanglement.