Entangled neutrinos in a supernova

Abstract

We consider the entanglement of neutrinos evolving adiabatically under the effect of vacuum oscillations and self interactions through decreasing neutrino density similar to a core collapse supernova. For an initial state which consists only of electron type neutrinos, we analytically calculate the asymptotic value of the entropy of entanglement between the lowest energy neutrino and the rest of the system as a function of the number of neutrinos. We find that, as we increase neutrino number the entanglement entropy grows at first. But after going through a maximum, it approaches to zero in the limit of infinite number of neutrinos. We find that the number of neutrinos for which the entropy maximizes depends on the mixing angle.