Entanglement in Collective Neutrino Oscillations on a Quantum Computer
Simulations on a quantum computer have been propounded as a next-generation tool for studying neutrino flavour oscillations in dense environments like supernovae or neutron star mergers. However, quantum advantage hinges on the presence of quantum entanglement in the neutrino ensemble, and it has been argued that such entanglement becomes negligible in the limit of large neutrino number density. Here, we address this question by explicitly simulating the multiparticle dynamics of entangled neutrino ensembles with a varying number of particles, $N$, on both classical and quantum hardware, and comparing our results to those obtained with conventional ``mean-field'' methods based on Boltzmann-type kinetic equations. For simple toy systems, we demonstrate both analytically and numerically that, indeed, the predictions of full multiparticle simulations agree with those of mean-field methods in the large-$N$ limit. Along the way, we develop novel algorithms for the efficient simulation of entangled neutrino gases on both classical and quantum hardware. We then discuss physical situations in which an entangled neutrino system \emph{cannot} be described through mean-field dynamics alone and quantum entanglement therefore becomes phenomenologically relevant. We comment on the conditions under which these scenarios may be realized in supernova cores or neutron star mergers.