Separability and entanglement in 2x2xN composite quantum systems

Abstract

We investigate separability and entanglement of mixed states in ${\mathcal{C}}^2\otimes {\mathcal{C}}^2\otimes {\mathcal{C}}^N$ three party quantum systems. We show that all states with positive partial transposes that have rank $\le N$ are separable. For the 3 qubit case (N=2) we prove that all states $\rho$ that have positive partial transposes and rank 3 are separable. We provide also constructive separability checks for the states $\rho$ that have the sum of the rank of $\rho$ and the ranks of partial transposes with respect to all subsystems smaller than 15N-1.

Finally corrected file submitted. Numerous misprints and small errors corrected, better versions of constructive separability checks included, updated and extended references

References in corpus (1)

• Classification of mixed three-qubit states

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