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We present and discuss different protocols for preparing an arbitrary quantum state of a qubit using only a restricted set of measurements, with no unitary operations at all. We show that an arbitrary state can indeed be prepared, provided that the available measurements satisfy certain requirements. Our results shed light on the role that measurement-induced back-action plays in quantum feedback control and the extent to which this back-action can be exploited in quantum-control protocols.doi:10.1103/physreva.82.062103 fatcat:mqbukpbe7ne5dmre3qhyl7q6te