Abstract. We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way, and show that they generate extreme rays in the cone of all positive semi-definite matrices with positive partial transposes. They also have Schmidt numbers two.

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An ionic liquid (IL) 1-butyl-3-methylimidazoliumtetrafluoroborate (BMIM + BF 4 À )/CuO composite was prepared for CO 2 transport membranes. CuO nanoparticles (NPs) were successfully generated in BMIM + BF 4 À . The formation of CuO NPs was ascribed to the favorable interaction between the ions of BMIM + BF 4 À and the surface of the CuO particles. To confirm the coordination behavior of the BMIM + BF 4 À /CuO membrane, TGA and FT-Raman spectroscopy were employed. The ideal CO 2 /N 2 selectivity in the case of the composite material was 21.0, with a CO 2 permeance of 52.4 GPU, while the neat BMIM + BF 4 À membrane showed a selectivity of 5.0 and a CO 2 permeance of 17.0 GPU. The enhanced separation performance was attributed to (1) the synergistic effect of well-dispersed CuO nanoparticles, resulting in enhanced CO 2 solubility due to the increased surface of the oxide particle layer and (2) the abundant free ions in BMIM + BF 4 À .