Exposedness of elementary positive maps between matrix algebras

Abstract

The positive linear maps $\ad_s$ which send matrices $x$ to $s^{\ast }xs$ 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.

arXiv comment9 pages