Critical Point in the Problem of Maximizing the Transition Probability Using Measurements in an n-Level Quantum System

Abstract

We consider the problem of maximizing the transition probability in an n-level quantum system from a given initial state to a given final state using nonselective quantum measurements. We find a sequence of measurements that is a critical point of the transition probability and, moreover, a local maximum in each variable on the set of one-dimensional projectors. We consider the class of one-dimensional projectors because these projectors describe the measurements of populations of pure states of the system.