Quantum magic and computational complexity in the neutrino sector

We consider the quantum magic in systems of dense neutrinos undergoing coherent flavor transformations, relevant for supernova and neutron-star binary mergers. Mapping the three-flavor-neutrino system to qutrits, the evolution of quantum magic is explored in the single scattering angle limit for a selection of initial tensor-product pure states for Nν≤8 neutrinos. For |νe〉⊗Nν initial states, the magic, as measured by the α=2 stabilizer Renyi entropy M2, is found to decrease with radial distance from the neutrino sphere, reaching a value that lies below the maximum for tensor-product qutrit states. Further, the asymptotic magic per neutrino, M2/Nν, decreases with increasing Nν. In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic M2/Nν increasing with Nν. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.