The problem of classification of decomposable (in the sense of Stormer) positive maps between matrix algebras is presented. We propose the new notion of "finite" version of decomposability ( $k$ -decomposabilty). The characterisation of $k$ -decomposability on the Hilbert space level is done. In the case of low dimensional algebras the notion of local decomposability and its applications for the description of decomposable maps are discussed.The problem of classification of decomposable (in the sense of Stormer) positive maps between matrix algebras is presented. We propose the new notion of "finite" version of decomposability ($k$-decomposabilty). The characterisation of $k$-decomposability on the Hilbert space level is done. In the case of low dimensional algebras the notion of local decomposability and its applications for the description of decomposable maps are discussed.

arXiv:quant-ph/0411035Quantum Probability and Infinite Dimensional AnalysisJan 1, 20059 citations

On positive decomposable maps

W.A. Majewski

arXiv:quant-ph/0603008Reports on Mathematical PhysicsJun 1, 20075 citations

ON POSITIVE MAPS: PPT STATES AND ENTANGLEMENT

W. A. Majewski

Quantum Bio-InformaticsJan 1, 20100 citations

The problem of classification of decomposable (in the sense of Stormer) positive maps between matrix algebras is presented. We propose the new notion of "finite" version of decomposability (

k

-decomposabilty). The characterisation of

k

-decomposability on the Hilbert space level is done. In the case of low dimensional algebras the notion of local decomposability and its applications for the description of decomposable maps are discussed.