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.

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

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• Entangled symmetric states of N qubits with all positive partial transpositions
• Characterization of Distillable and Activable States using Entanglement Witnesses
• Unique decompositions, faces, and automorphisms of separable states
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• Searching for extremal PPT entangled states
• Separability and entanglement in 2x3xN composite quantum systems
• Unextendible product bases, bound entangled states, and the range criterion
• Multi-partite separable states with unique decompositions and construction of three qubit entanglement with positive partial transpose
• Separability of Multipartite Quantum States with Strong Positive Partial Transpose
• Extremal states of positive partial transpose in a system of three qubits
• Classification of mixed high-dimensional multiparticle systems
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• Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities
• Derivation of the robustness from the concurrence
• Separability and Entanglement of Identical Bosonic Systems