Probing $CP$ violation and mass ordering in neutrino oscillations in matter through quantum speed limits

TL;DR

This paper explores how quantum speed limits can be used to analyze $CP$ violation and mass ordering in neutrino oscillations, revealing differences in evolution times and entanglement between scenarios relevant to current and future experiments.

Contribution

It introduces the use of quantum speed limits as an analytical tool to distinguish neutrino mass orderings and $CP$ violation effects in matter, connecting theoretical bounds with experimental observables.

Findings

Faster neutrino state evolution in normal mass ordering.

Differences in quantum speed limits between mass orderings.

Fast entanglement suppression in DUNE with normal ordering.

Abstract

The quantum speed limits (QSLs) set fundamental lower bounds on the time required for a quantum system to evolve from a given initial state to a final state. In this work, we investigate $CP$ violation and the mass ordering problem of neutrino oscillations in matter using the QSL time as a key analytical tool. We examine the QSL time for the unitary evolution of two- and three-flavor neutrino states, both in vacuum and in the presence of matter. Two-flavor neutrino oscillations are used as a precursor to their three-flavor counterparts. We further compute the QSL time for neutrino state evolution and entanglement in terms of neutrino survival and oscillation probabilities, which are experimentally measurable quantities in neutrino experiments. A difference in the QSL time between the normal and inverted mass ordering scenarios, for neutrino state evolution as well as for entanglement, under the effect of a $CP$ violation phase is observed. Our results are illustrated using the length scales and energies of ongoing long-baseline accelerator neutrino experiments such as T2K, NOvA, and the upcoming DUNE experiment. Notably, three-flavor neutrino oscillations in constant matter density exhibit faster state evolution across all these neutrino experiments in the normal mass ordering scenario. Additionally, we observe fast entanglement suppression in DUNE assuming a normal mass ordering.