Quantum Magic and Computational Complexity in the Neutrino Sector

• URL: http://arxiv.org/abs/2411.04203v1
• Date: Wed, 06 Nov 2024 19:02:30 GMT
• Title: Quantum Magic and Computational Complexity in the Neutrino Sector
• Authors: Ivan Chernyshev, Caroline E. P. Robin, Martin J. Savage,
• Abstract summary: Mapping the three-flavorneutrino system to qutrits, the evolution of quantum magic is explored. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.
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• Abstract: 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 $N_\nu \le 8$ neutrinos. For $|\nu_e\rangle^{\otimes N_\nu}$ initial states, the magic, as measured by the $\alpha=2$ 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, $M_2/N_\nu$, decreases with increasing $N_\nu$. In contrast, the magic evolving from states containing all three flavors reaches values only possible with entanglement, with the asymptotic $M_2/N_\nu$ increasing with $N_\nu$. These results highlight the connection between the complexity in simulating quantum physical systems and the parameters of the Standard Model.

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