Classification of Quantum Separable States in Multipartite Quantum Systems

To study the separability of quantum states in multipartite quantum systems, the classification of multipartite quantum separable states was presented by using Bell inequalities. These inequalities can well distinguish all possible k-separable states in 2⊗2⊗2⊗2⊗2 systems, including fully separable, biseparable, tri-separable and four-separable states. Using the generalized Bell operator and the classification of genuine entanglement, applying the Cauchy-Schwarz inequality, the linear programming and other methods in mathematics, the authors give out the upper bound of absolute value for the average values of Bell operator to achieve the classification of separable states in multipartite quantum systems.