Geuine tripartite entanglement in three-flavor neutrino oscillations

TL;DR

This paper investigates the genuine tripartite entanglement in three-flavor neutrino oscillations using a new measure called concurrence fill, revealing its effectiveness in quantifying quantum resources in neutrino experiments.

Contribution

It introduces and applies the concurrence fill measure to quantify tripartite entanglement in neutrino oscillations, comparing it with other measures and highlighting its advantages.

Findings

Concurrence fill reaches 0.89 for electron antineutrino oscillations.

Concurrence fill outperforms other measures in quantifying quantum resources.

Tripartite entanglement measures show different behaviors in smoothness and peaks.

Abstract

The violation of Leggett-Garg inequalities tested the quantumness of neutrino oscillations (NOs) across macroscopic distances. The quantumness can be quantified by using the tools of the quantum resource theories. Recently, a new genuine tripartite entanglement measure [S. B. Xie et al., Phys. Rev. Lett. 127, 040403 (2021)], concurrence fill, is defined as the square root of the area of the concurrence triangle satisfying all genuine multipartite entanglement conditions. It has several advantages compared to other existing tripartite measures. Here, we focus on using concurrence fill to quantify the tripartite entanglement in three-flavor NOs. Concurrence fill can reach its maximum $0.89$ for the experimentally-observed electron antineutrino oscillations, but it cannot for the muon antineutrino oscillations. In both cases, we compare its performance with other three tripartite entanglement measures, including the generalized geometric measure (GGM), the three-$\pi$ entanglement, and the genuinely multipartite concurrence (GMC), in the neutrino propagation, and accordingly show that concurrence fill contains the most quantum resource. Furthermore, concurrence fill and the three-$\pi$ entanglement are always smooth, while GGM and GMC measures have several sharp peaks. The genuine tripartite quantification of the quantumness of three-flavor NOs represents the first step towards the further potential application of neutrinos on quantum information processing.