Computing the quantumguesswork: a quadratic assignment problem

The quantum guesswork quantifies the minimum number of queries needed to guess state a ensemble if one is allowed query only at time. Previous approaches computation were based on standard semi-definite programming techniques and therefore lead approximated results. In contrast, we show that computing qubit ensembles with uniform probability distribution corresponds solving quadratic assignment problem provide an algorithm that, upon input any over discrete ring, after finitely many steps outputs exact closed-form expression its guesswork. While in general complexity our guesswork-computing factorial states, main result consists showing more-than-quadratic speedup for symmetric ensembles, scenario corresponding three-dimensional analog maximization version turbine-balancing problem. To find such symmetries, point set symmetries. symmetries-finding polynomial points. As examples, compute regular quasi-regular sets states.