In quantum information theory Zeuner's conjecture posits the existence of SIC-POVMs -- or symmetric, informationally complete, positive operator-valued measures -- for every finite-dimensional Hilbert space. These can be important for quantum measurements, and have several applications in the context of quantum state tomography and quantum cryptography.
While the conjecture is unproven, exact expressions for SIC-POVMs have been found in all dimensions up to 53, and in some higher dimensions as large as 5779, and numerical solutions have been found up to dimension 193. There exists a translation of the problem into a (difficult) numerical minimisation problem, which we want to investigate with modern search algorithms, along with theoretical studies of the symmetries of the problem to more easily find new, both numerical and exact, solutions.