Exposedness of elementary positive maps between matrix algebras

Seung-Hyeok Kye

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arXiv · 2301.05788

Exposedness of elementary positive maps between matrix algebras

Seung-Hyeok Kye

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Abstract

The positive linear maps $\ad_s$ which send matrices $x$ to $s^*xs$ play important roles in quantum information theory as well as matrix theory. It was proved by Marciniak [Linear Multilinear Alg. 61 (2013), 970--975] that the map $\ad_s$ generates an exposed ray of the convex cone of all positive linear maps. In this note, we provide two alternative proofs, using Choi matrices and Woronowicz's method, respectively.

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Seung-Hyeok Kye. 2023-01-13. Exposedness of elementary positive maps between matrix algebras. https://arxiv.org/abs/2301.05788

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