Simulation of open quantum dynamics in Markovian environment

Although conditions for controllability of quantum systems are well studied, most of them consider the infinite time horizon, i.e., whether certain operations are possible given enough time. In this article, I propose a framework studying all the possible operations one can generate at given finite time on a quantum system in Markovian environment. I give a complete characterization of the operations one can simulate at any given time on a qubit in unital Markovian environment and discuss possible extensions.