Quantum measurement optimization by decomposition of measurements into extremals

Using the convex structure of positive operator value measurements and of several quantities used in quantum metrology, such as quantum Fisher information or the quantum Van Trees information, we present an efficient numerical method to find the best strategy allowed by quantum mechanics to estimate a parameter. This method explores extremal measurements thus providing a significant advantage over previously used methods. We exemplify the method for different cost functions in a qubit and in a harmonic oscillator and find a strong numerical advantage when the desired target error is sufficiently small.