 
Summary: Coherent control of open quantum dynamical systems
Claudio Altani
SISSAISAS
International School for Advanced Studies
via Beirut 24, 34014 Trieste, Italy
A systematic analysis of the behavior of the quantum Markovian master equation driven by
coherent control elds is proposed. Its irreversible character is formalized using controltheoretic
notions and the sets of states that can be reached via coherent controls are described. The analysis
suggests to which extent (and how) it is possible to counteract the eect of dissipation.
PACS numbers: 03.65.Yz, 03.67.Pp, 03.67.Lx
I. INTRODUCTION
For an open quantum dynamical system, see [1{3], the problem of coherent manipulation of the state
is far less trivial than for a closed system and is the subject of recent intense research, especially but not
exclusively in connection with quantum information processing, see [4{6] or the survey papers [7, 8]. The
(wellknown) reason is that the dissipation/relaxation part of the dynamics (often called the Lindbladian)
tends irreversibly to bring the system to an equilibrium point which cannot be fully compensated by means
of coherent control authority, although it can be modied to some extent, see [9]. For the Markovian
formulation, this is encoded in the structure of the Lindbladian. In this work, the idea of \irreversibility in
spite of the control action" is made rigorous by using standard notions from classical control theory. For
example, it is shown that the sets of states reachable by means of coherent controls are almost always open
