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< 8 neutrinos. For initial states of electron-type neutrinos, the magic, as measured by the M(2) stabilizer Renyi entropy, 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, decreases with increasing N. In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic M(2)/N increasing with N. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.
We would like to thank Vincenzo Cirigliano, Henry Froland and Niklas Müller for useful discussions, as well as Emanuele Tirrito for his inspiring presentation at the IQuS workshop Pulses, Qudits and Quantum Simulations, co-organized by Yujin Cho, Ravi Naik, Alessandro Roggero and Kyle Wendt, and for subsequent discussions, an also related discussions with Alessandro Roggero and Kyle Wendt. We would further thank Alioscia Hamma, Thomas Papenbrock and Rahul Trivedi for useful discussions during the IQuS workshop Entanglement in Many-Body Systems: From Nuclei to Quantum Computers and Back, co-organized by Mari Carmen Bañuls, Susan Coppersmith, Calvin Johnson and Caroline Robin. This work was supported by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science, and by the Department of Physics and the College of Arts and Sciences at the University of Washington (Ivan and Martin). This work was also supported, in part, by Universität Bielefeld, and by ERC-885281-KILONOVA Advanced Grant (Caroline). This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 using NERSC awards NP-ERCAP0027114 and NP-ERCAP0029601.
