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arXiv:quant-ph/0102115 · Physical Review A

Separability and entanglement in C2⊗C2⊗CN composite quantum systems

Siniša Karnas, Maciej Lewenstein

Published Sep 18, 2001• 26 citations
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Abstract

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

DOI
10.1103/physreva.64.042313

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