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Strong subadditivity inequality for a three-particle composite system is animportant inequality in quantum information theory which can be studied via afour-particle entangled state. We use two three-level atoms in $\Lambda$configuration interacting with a two-mode cavity and the Raman adiabaticpassage technique for the production of the four-particle entangled state.Using this four-particle entanglement, we study for the first time variousaspects of the strong subadditivity inequality.Comment: 5 pages, 3 figures, RevTeX4, submitted to PR

Strong subadditivity inequality for quantum entropies and four-particle entanglement