Entanglement in interference-based quantum control: the wave function is not enough.

We analyze the way entanglement affects features of interference-based quantum control. We show that quantum interferences vanishes in several cases in the process of extracting probabilities from wave functions. As an example, we discuss the loss of quantum interferences when tracing over number states of the radiation field. We also consider the way in which controllability is reduced when tracing over an entire manifold of states whose cumulative probability we wish to control. Finally, we show that it is impossible to control the relative populations of degenerate states (occurring, e.g., in dissociation and chemical reactions) when the relevant transition amplitude is factorizeable, i.e., when it can be written as a product of a purely classical field-dependent part and a purely materialdependent part. Differences between entanglement and non-factorizability of amplitudes are emphasized.