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 $N_ν\le 8$ neutrinos. For $|ν_e\rangle^{\otimes N_ν}$ initial states, the magic, as measured by the $α=2$ stabilizer Renyi entropy $M_2$, 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, $M_2/N_ν$, decreases with increasing $N_ν$. In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic $M_2/N_ν$ increasing with $N_ν$. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.