Notes on completely positive maps and continuous-time Markovian CP evolution. A geometry-flavored perspective

Abstract

These notes provide a detailed and self-contained exposition of basic theory of CP maps and continuous-time Markovian evolution.The infinite-dimensional (separable) setting is handled as an extension of the finite-dimensional one.The treatment stands on two legs.For the finite-dimensional part, a basis-free version of the Choi-Jamiolkowski isomorphism called simply Jamiolkowski transform.And, for the extension, the ground matrix element topology (GMET), which does for the superoperators on trace-class operators what the weak-operator topology does for bounded operators on a Hilbert space. Background in open quantum systems or quantum information theory is not assumed.