Separability and entanglement in 2x2xN composite quantum systems

Original · EN

We investigate separability and entanglement of mixed states in C²⊗ C²⊗ Cⁿ three party quantum systems. We show that all states with positive partial transposes that have rank ≤ N are separable. For the 3 qubit case (N=2) we prove that all states ρ that have positive partial transposes and rank 3 are separable. We provide also constructive separability checks for the states ρ that have the sum of the rank of ρ and the ranks of partial transposes with respect to all subsystems smaller than 15N-1.