We consider a quantum dot in a semiconductor device P and a sequence of probes sent to interact with it. After each probe interacts with P, a projective measurement is performed on the probe. This process generates a discrete stochastic process of density matrices, ρn. We prove that the density matrices ρn purify as n tends to infinity. Our results provide a mathematical framework to understand phenomena analogous to those explored in the experiments of Haroche and Wineland, which were awarded the Nobel Prize in Physics in 2012.
