A numerical solution for the accessible quantum information problem

The quantum discrimination problem is an important topic of quantum information theory. Discriminating among a set of M non-orthogonal quantum states means choosing among one of them based on a quantum measurement. In order to accomplish this task one must choose a measure of information to rank the potential solutions. When the Shannon mutual information is considered as such a measure one has an accessible information problem. The accessible information problem consists on the maximization of the mutual information over all sorts of quantum measurements. Analytical solutions for this optimization problem are not available for the general case. Even numerical solutions are hard to find because of the nonlinear nature of the mutual information function. On the other hand, genetic algorithms work pretty well with "misbehaved" functions. Based on the previous statements, we propose solving the accessible information problem via genetic algorithms.