  In this work, we address the problem of maximizing fidelity in a quantum
state transformation process controlled in such a way as to keep decoherence
within given bounds. We consider a three-level $\Lambda$-type atom subjected to
Markovian decoherence characterized by non-unital decoherence channels. We
introduce fidelity as the performance index for the quantum state
transformation process since the goal is to maximize the similarity of the
final state density operator with the one of the desired target state. We
formulate the quantum optimal control problem with state constraints where the
later reflect the fact that the decoherence level remains within a pre-defined
bound. Optimality conditions in the form of a Maximum Principle of Pontryagin
in Gamkrelidze's form are given. These provide a complete set of relations
enabling the computation of the optimal control strategy. This is a novel
approach in the context of quantum systems.
