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Indistinguishability of identical particles is a resource for quantum information processing and has been utilized to generate entanglement from independent particles that spatially overlap only at the detection stage. Here we provide a general controllable scheme capable of generating, from a pure product state of N qubits, a comprehensive class of multipartite entangled states, including W, Dicke, GHZ, and cluster states with both bosonic and fermionic statistics within the framework of spatially localized operations and classical communication (sLOCC). Using graph-based representations of the sLOCC framework, we translate the generation schemes of specific entangled states into colored, complex, and weighted digraphs, each corresponding to a given experimental setup. This graph-theoretical approach allows for precise targeting of particular multipartite states, exploration of diverse generation schemes, and optimization of generation efficiency. Our results demonstrate that the indistinguishability of identical graph nodes in quantum networks offers useful perspectives for photonic technology.
Mahdavipour et al. (Mon,) studied this question.