Efficient Dicke-state distribution in a network of lossy channels

We analyze the generation of entanglement in a multipartite optical network. We generalize the twin-field strategy to the multipartite case and show that our protocol has advantageous rate-loss scalings of distributing W states and Dicke states over the star networks. We provide precise theoretical formulas and quantitative performance analyses. Also, analysis of the same protocol using Gaussian states as resources, which is a typical setup in many experimental tests, is provided. We numerically study the feasibility of the protocol in realistic experimental conditions with imperfect detectors. We observe that the advantage depends on the chosen fidelity and is affected by the dark counts of the detector.