  We study the problem of driving an unknown initial mixed quantum state onto a
known pure state without using unitary transformations. This can be achieved,
in an efficient manner, with the help of sequential measurements on at least
two unbiased bases. However here we found that, when the system is affected by
a decoherence mechanism, only one observable is required in order to achieve
the same goal. In this way the decoherence can assist the process. We show
that, depending on the sort of decoherence, the process can converge faster or
slower than the method implemented by means of two complementary observables.
