Quantum Experiments and Graphs: Multiparty States as coherent superpositions of Perfect Matchings

Understand

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory.

• In these setups, the paths of photons are identified such that the photon-source information is never created.
• We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup.
• Every term in the emerging quantum superposition corresponds to a perfect matching in the graph.