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The generation of entangled quantum states of photons is a key capability for a vast range of technologies and forms the foundations of quantum communication, computation, and metrology. In photonics, due to the lack of strong photon-photon interactions, the generation of the vast majority of entangled states is probabilistic. This typically requires post-selection to identify successful generation events, destroying the target state. Fortunately, there exists an alternative solution: Heralding. Here, the measurement of ancillary photons in auxiliary modes indicates that the generated state exists, without the need to measure and thereby destroy it.
In this work, we report a protocol for generating heralded multi-mode two-photon entangled NOON states [1], coherent superpositions of N photons across multiple modes, integral resources for applications including multiphase estimation and distributed sensing. We demonstrate the protocol by experimentally generating and verifying a three-mode two-photon NOON state, whose presence is signalled by the detection of a single photon in an auxiliary mode. To validate the generated state, we perform a tailored measurement to estimate its fidelity relative to an ideal three-mode NOON state, yielding $0.823\pm0.018$. Furthermore, with this achieved fidelity, the generated state exceeds the threshold for genuine multipartite entanglement by more than 8 standard deviations. We then theoretically show how to scale the protocol to generate arbitrary $d$-mode two-photon NOON states using a cascaded linear-optical scheme. Due to the low resource overhead (only one ancillary photon) and high success probability ($P=25\%$) of our demonstration, and the protocol's scalability, our work provides an experimental and theoretical advance for multi-mode entanglement generation. This generation of multimode entangled states represents a key milestone in linear-optical quantum information realisable with current technology and highlights these states as resources for entangled multi-qubit protocols.
[1] Singh, Sukhjit P., et al. "Heralded generation of a three-mode NOON state." arXiv preprint arXiv:2512.08458 (2025).
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