Exposedness of elementary positive maps between matrix algebras
Seung-Hyeok Kye · Linear and Multilinear Algebra · 2024
The positive linear maps Ads which send matrices x to s∗xs play important roles in quantum information theory as well as matrix theory. It was proved by [Marciniak M. Rank properties of exposed positive maps. Linear Multilinear Alg. 2013;61:970–975] that the map Ads 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.