Oscillations of the purity in the repeated-measurement-based generation   of quantum states
  Repeated observations of a quantum system interacting with another one can drive the latter toward a particular quantum state, irrespectively of its initial condition, because of an {\em effective non-unitary evolution}. If the target state is a pure one, the degree of purity of the system approaches unity, even when the initial condition of the system is a mixed state. In this paper we study the behavior of the purity from the initial value to the final one, that is unity. Depending on the parameters, after a finite number of measurements, the purity exhibits oscillations, that brings about a lower purity than that of the initial state, which is a point to be taken care of in concrete applications. 
B. Militello, K. Yuasa, H. Nakazato, and A. Messina