Trade-off relations of quantum resource theory in neutrino oscillations

TL;DR

This paper investigates the trade-off relations of quantum resources in neutrino oscillations, revealing how quantum coherence and entanglement distribute and convert during neutrino propagation, with implications for quantum information processing.

Contribution

It introduces analytical trade-off relations of quantum resources in three-flavor neutrino oscillations based on Bell violations, coherence, and concurrence, advancing understanding of quantum resource dynamics in neutrinos.

Findings

Sum of maximal CHSH violations ≤ 12 for flavor pairs

Existence of an equality relation between coherence and concurrence

Tripartite coherence ≥ sum of bipartite coherences

Abstract

The violation of the classical bounds imposed by Leggett-Garg inequalities has tested the quantumness of neutrino oscillations (NOs) over a long distance during the propagation. The measure of quantumness in experimentally observed NOs is studied via quantum resource theory (QRT). Here, we focus on the trade-off relations of QRT in the three-flavor NOs, based on Bell-type violations, first-order coherence and intrinsic concurrence, and the relative entropy of coherence. For the electron and muon antineutrino oscillations, the analytical trade-off relations obeyed by the Bell-CHSH inequality of pairwise flavor states in this three-flavor neutrino system are obtained; the sum of the maximal violation of the CHSH tests for three pairwise flavor states is less than or equal to 12. Moreover, there exists an equality relation concerning first-order coherence and intrinsic concurrence in NOs, showing how much quantum resources flow between first-order coherence and intrinsic concurrence during the neutrino propagation. In addition, it is found that the tripartite coherence of three-flavor system is equal to or larger than the sum of the coherence of reduced bipartite flavor states. The trade-off relations of QRT provide a method for studying how the quantum resources convert and distribute in NOs, which might inspire the future applications in quantum information processing using neutrinos.