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Explicit separable density matrices, for mixed two qubits states, are derivedby the use of Hilbert Schmidt decompositions and Peres Horodecki criterion. Astrongly separable two qubits mixed state is defined by multiplications of twodensity matrices given with pure states while weakly separable two qubits stateis defined by multiplications of two density matrices which includes non-purestates. We find the sufficient and necessary condition for separability oftwo-qubits density matrices and show that under this condition the two-qubitdensity matrices are strongly separable.

Strong and weak separability conditions for two-qubits density matrices