Probe-mediated control of quantum systems

We study a new approach to the control of a quantum system S, which uses the coupling of S with a quantum probe P, rather than a direct action on S. The external control affects only P, and the accessibility and controllability properties describe to what extent it is possible to drive the state of S by varying the initial state of P and using the interaction between the two systems. In particular, we study the case of two-dimensional system and probe. Two situations are considered: either the total system S+P is a closed one, or it is surrounded by a bath of decoupled harmonic oscillators. We give results on the controllability and accessibility properties of this scheme, and we discuss the relation of these properties with the entangling capability of the interaction between S and P. In particular, we show that the SWAP operator plays a special role