Entanglement of formation is a fundamental measure that quantifies the entanglement of bipartite quantum states. This measure has recently been extended into multipartite states, taking the name a-entanglement of formation. In this work we follow an analogous multipartite extension for the Gaussian version of entanglement of formation, and focusing on the finest partition of a multipartite Gaussian state, we show that this measure is fully additive and computable for three-mode Gaussian states.
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