Deterministic multipartite magnonic entanglement in a cavity optomagnonic network

Distributing entanglement among distant quantum nodes is essential for building scalable quantum networks. In this paper we propose a scheme to generate multipartite magnonic entanglement in a cavity optomagnonic network via measurement-based feedback. We consider $N$ spatially separated cavity optomagnonic systems and the cavity outputs are coupled through a beam-splitter array. The fields from the array's output ports are subjected to continuous homodyne detection, and the measurement outcomes are fed back to the systems. We analytically demonstrate that multipartite magnonic entanglement can be deterministically generated in the present scheme by tuning the local phases of homodyne detection appropriately. The multipartite entanglement arises from photon-magnon entanglement, which is distributed among the magnonic modes via the beam-splitter-array interferometric measurement. We further reveal that the multipartite entanglement is optimized when the cavity field couples to the magnonic mode via a two-mode squeezing interaction in each cavity optomagnonic system, because such an interaction induces optimal magnonic squeezing when homodyning the cavity output. The present scheme can be directly extended to other light-matter systems for realizing multipartite entanglement of continuous variables. Beyond advancing fundamental quantum research, this work provides a practical platform for magnon-based quantum technologies.