Quantum Probability and Applications

After more than one century since the beginning of quantum theory and after almost forthy years of intense mathematical development, European universities should no longer neglect, in their curricula for teaching probability theory at undergraduate (and often graduate and post-graduate) level the deep conceptual and technical changes that have post-graduate) level the deep conceptual and technical changes that have occurred in our understanding of the law of chances after the birth of quantum mechanics. The fact that the most advanced contemporary physical theory, quantum mechanics, uses for its statistical predictions a probabilistic model completely different from the one that is taught in standard curricula is an historical paradox that should be amended. This is also an occasion to propose a curriculum with a richer and more varied offer which should encourage young students to choose a specialized field of mathematics not only with the idea of pursuing an academic carrier but also envisaging the possibility of putting their expertise at the service of concrete industrial projects. Some of our group are already experimenting this scheme since several years in isolated projects: this program is the first collective attempt of the European quantum probability network to implement this program beyond pure research and including teaching and industrial projects. The elaboration of a new (or at least an integration of the old) curriculum in probability theory is an ambitious task that requires deep competences in the most advanced research in the topic in object, long experience in applied and industrial projects, familiarity with the multi-disciplinary and multi-national training at all university levels.