Driving a known state by a discrete sequence of direct measurements

Abstract

We study the problem of driving a known initial quantum state onto a known pure state without resorting to unitary transformations. This task can be achieved by means of a discrete sequence of von Neumann measurements only, introducing $N$ observables which are consecutively measured in order to make the state of the system approach the target state. We show that the probability of projecting onto the target state can be increased meaningfully by adding suitable observables to the process, that is, it converges to 1 when $N$ increases. These observables depend on the initial state and on the target state. We compare this scheme with one for which the initial state is not known [see L. Roa et al., Phys. Rev. A 73, 012322 (2006)]. This comparison shows that the knowledge of the initial density operator does not always increase the probability of success.