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Abstract

We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multiphoton sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such a general graph description provides new insights for producing complex high-dimensional multiphoton quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, the properties of hypergraphs can be investigated experimentally. For example, the NP-complete problem of deciding whether a hypergraph has a perfect matching can be answered by experimentally detecting multiphoton events in quantum experiments. By introducing complex weights in hypergraphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multiphoton high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings.