This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the system, we explicitly show how to construct a Kraus map that transforms one state into another. Moreover, we prove by construction the existence of a Kraus map that transforms all initial states into a predefined target state (such a process may be used, for example, in quantum information dilution). Thus, in sharp contrast to unitary control, Kraus-map dynamics allows for the design of controls which are robust to variations in the initial state of the system. The capabilities of non-unitary control for population transfer between pure states illustrated for an example of a two-level system by constructing a family of nonunitary Kraus maps to transform one pure state into another. The problem of dynamic state controllability of open quantum systems (i.e., controllability of state-to-state transformations, given a set of available dynamical resources such as coherent controls, incoherent interactions with the environment, and measurements) is also discussed.

No abstract

International audienceA connectivity analysis of controlled quantum systems assesses the feasibility of a field existing that can transfer at least some amplitude between any specified pair of states. Although Hamiltonians with special structure or symmetry may not produce full connectivity, it is argued and demonstrated that virtually any Hamiltonian is expected to be connected. The connectivity of any particular system is generally revealed in the quantum evolution over a single or at most a few time steps. A connectivity analysis is inexpensive to perform and it can also identify statistically significant intermediate states linking a specified initial and final state. These points are illustrated with several simple systems. The likelihood of an arbitrary system being connected implies that at least some product yield can be expected in the laboratory for virtually all systems subjected to a suitable control