  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.
