A differentiable SDP method generates positive non-decomposable maps, identifies parametrized families, and explores open problems like the PPT square conjecture.
$k$-decomposability of positive maps
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abstract
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.
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quant-ph 1years
2026 1verdicts
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Generating Non-Decomposable Maps with Differentiable Semidefinite Programming
A differentiable SDP method generates positive non-decomposable maps, identifies parametrized families, and explores open problems like the PPT square conjecture.