Additivity Relations of Quantum Correlations for Three-qubit Entangled State in Atom-cavity System

Taking advantage of quantum discord and negativity respectively, four additivity relations of quantum correlations are studied in the atom-cavity system, for three identical two-level atoms resonantly interact with a single-mode high-Q cavity simultaneously. Through numerical analysis, we find that in this model of atom-cavity system, four additivity relations of negativity are always satisfied well, no matter tripartite are in the pure states or the mixed states, while the results of quantum discord are not always satisfied. What’s more, if and only if the mixed three-atom states evolve into the pure states again, four additivity inequality relations of quantum discord and negativity become equalities simultaneously.