The strong subadditivity inequality for a three-particle composite system is an important inequality in quantum information theory which can be studied via a four-particle entangled state. We use two three-level atoms in [Formula Presented] configuration interacting with a two-mode cavity and the Raman adiabatic passage technique for the production of the four-particle entangled state. Using this four-particle entanglement, we study various aspects of the strong subadditivity inequality. 2003 The American Physical Society.