Analyzing multipartite entanglement via Schmidt decomposition in pure non-Gaussian three-mode states

We investigate the distribution of entanglement in a system of three interacting quantum particles modeled as coupled harmonic oscillators using the Schmidt decomposition formalism. This approach enables us to represent the multipartite quantum state as a sum of product states between subsystems. The Schmidt coefficients precisely measure quantum correlations. By analyzing how these coefficients evolve as inter-oscillator coupling strengths vary, we reveal how entanglement is shared and redistributed across different bipartitions of the system. Through detailed numerical simulations, we identify coupling regimes that enhance, suppress, or destabilize entanglement, revealing the intricate structure of multipartite quantum correlations. Our findings provide valuable insights into controlling, and optimizing entanglement in networked quantum architectures. They offer practical guidance for quantum information processing and communication protocols. In the appropriate limit, our analysis naturally recovers known results for two coupled oscillators, thus validating the generality of our approach.