Separability and entanglement inC2⊗C2⊗CNcomposite quantum systems

Siniša Karnas, Maciej Lewenstein
2001 Physical Review A. Atomic, Molecular, and Optical Physics  
We investigate separability and entanglement of mixed states in C^2⊗ C^2⊗ C^N 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.
doi:10.1103/physreva.64.042313 fatcat:zpo3ntost5c4rdcbjgwrsnbigi