Quantum Magic and Computational Complexity in the Neutrino Sector

TL;DR

This paper investigates the evolution of quantum magic in dense neutrino systems relevant for astrophysical phenomena, revealing how initial states and system size influence quantum complexity and entanglement.

Contribution

It introduces a mapping of three-flavor neutrino systems to qutrits and analyzes quantum magic evolution, highlighting differences based on initial flavor states and system size.

Findings

Magic decreases with distance for pure electron neutrino states.

Asymptotic magic per neutrino decreases with system size for pure states.

States with all three flavors exhibit magic indicative of entanglement.

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.