Strong and weak separability conditions for two-qubits density matrices

Explicit separable density matrices, for mixed–two-qubits states, are derived by using Hilbert-Schmidt (HS) decompositions and Peres-Horodecki criterion. A “strongly separable” two-qubits mixed state is defined by multiplications of two density matrices, given with pure states, while “weakly separable” two-qubits mixed state is defined, by multiplications of two density matrices, which includes non-pure states. We find the sufficient and necessary condition for separability of two qubits density matrices and show that under this condition the two-qubits density matrices are strongly separable.