Abstract
We study maximally multipartite-entangled states in the context of Gaussian continuous variable quantum systems. By considering multimode Gaussian states with constrained energy, we show that perfect maximally multipartite-entangled states, which exhibit the maximum amount of bipartite entanglement for all bipartitions, only exist for systems containing $n=2$ or 3 modes. We further numerically investigate the structure of these states and their frustration for $n\ensuremath{\le}7$.
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