arXiv:quant-ph/0510040

A reduction theorem for capacity of positive maps

Erling Størmer

Published Oct 6, 2005• 0 citations

Abstract

We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.

DOI: 10.48550/arxiv.quant-ph/0510040

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arXiv:quant-ph/0510040

A reduction theorem for capacity of positive maps

Erling Størmer

Published Oct 6, 2005• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.quant-ph/0510040

Related papers

A Reduction Theorem for Capacity of Positive Maps

Erling Størmer

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Erling Størmer

MATHEMATICA SCANDINAVICAMar 7, 20162 citations

Positive maps which are bijective on the set of rank projections

Erling Størmer

Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.Extending Wigner's theorem we give a characterization of positive maps of $B(H)$ into itself which map the set of rank k projections onto itself.

arXiv:1604.05717Apr 19, 20160 citations

Decomposable and atomic projection maps

Erling Størmer

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k-DECOMPOSABILITY OF POSITIVE MAPS

W. A. Majewski, Marcin Marciniak

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

Extending Wigner's theorem we give a characterization of positive maps of

B(H)

into itself which map the set of rank k projections onto itself.

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.