In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization, and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.
Paulo E. M. F. Mendonça, Alexei Gilchrist, and Andrew C. Doherty, Physical review A, 78, 012319, 2008. Copyright 2008 by the American Physical Society. The original article can be found at http://link.aps.org/doi/10.1103/PhysRevA.78.012319