The famous Lindblad, Kossakowski, Gorini, and Sudarshan's (LKGS) theorem characterizes the generator of a semigroup of completely positive maps. Motivated by this result we study the characterization of the generators of other positive maps e.g. k-positive and k-super positive maps. We prove a Schoenberg-type correspondence for a general non-unital semigroup of operators and apply this result to different cones of positive operators in $L(M_n, M_n)$ which are interesting for quantum information. As a corollary of our result, we re-establish the LKGS's theorem.
By Gilles Pisier
By Léonard Cadilhac
By Benjamin Anderson-Sackaney
By Zhendong Xu
By Purbayan Chakraborty
By Arthur Troupel
By Sara Azzali
By Zhenguo Wei
By Claudio Dappiaggi
