Heralded Generation of a Three-Mode NOON State

Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of postselection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823±0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our Letter provides a theoretical and experimental stepping stone for entangled multimode state generation, which is realizable with current technology. These multimode entangled states represent a key direction for linear optical quantum information that is complementary to multiqubit state encoding.