Control of open quantum systems

Control of atomic and molecular systems with quantum dynamics belongs to the field of quantum control which now attracts high interest of researchers. Highly investigates is the subject of coherent control of quantum systems which are isolated from the environment. Nowadays high interest is directed towards control of open, i.e. interacting with the environment, quantum systems. In this talk we will consider various ways for incoherent control of open quantum systems such as incoherent control by environment and by quantum measurements. We will also discuss the absence of traps for typical quantum control objective functionals in kinematic representation of the system dynamics by completely positive trace preserving maps and optimal approximation of quantum anti Zeno effect by any finite number of measurements.