Unifying First-Order Coherence, Concurrence, and Bell Correlations in Three-Flavor Neutrino Oscillations
Abstract
Neutrino oscillations provide a natural setting for investigating the quantum character of flavor conversion and the distribution of quantum resources over macroscopic distances. Here, we study exact relations among purity-based first-order coherence, pairwise concurrence, and the maximal Clauser-Horne-Shimony-Holt (CHSH) value in coherent three-flavor neutrino oscillations. By expressing the evolving neutrino as a three-qubit single-excitation state, we derive the generally mixed two-qubit reductions and show that the squared first-order coherence of each flavor mode and its two associated squared concurrences sum to unity. Furthermore, a closed two-branch relation is obtained, showing that the maximal CHSH value of any reduced pair is determined by its average first-order coherence and concurrence. The branch structure follows from the correlation-tensor spectrum and yields exact conditions for CHSH violation. For the vacuum parameters and propagation ranges considered, electron preparation gives weak CHSH violations in electroncontaining pairs, while muon preparation produces a dominant utau pair with substantially stronger concurrence and Bell correlations. The comparison also identifies the thirdflavor contribution responsible for the different locations of concurrence and CHSH maxima. These results clarify the distribution of quantum correlations during flavor evolution and provide a basis for extensions to coherent matter propagation and wave-packet-induced mixed states.
Related
- Response of Hellinger-distance based coherence to weak decoherence in two-flavor neutrino oscillations
- Separability and lower bounds of concurrence via symmetric measurement correlations
- When can decoherence reveal a Majorana phase? A phase-covariance no-go theorem for two-flavor neutrino oscillations
- Quantum field-theoretical description of solar neutrino oscillations
- Atmospheric Neutrino Oscillations: the Full Picture
BibTeX
@misc{li2026unifying,
title = {{Unifying First-Order Coherence, Concurrence, and Bell Correlations in Three-Flavor Neutrino Oscillations}},
author = {Bingbing Li and Tao Wu and Jiadong Shi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07285},
eprint = {2611.07285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07285},
}
RIS
TY - UNPB
TI - Unifying First-Order Coherence, Concurrence, and Bell Correlations in Three-Flavor Neutrino Oscillations
AU - Bingbing Li
AU - Tao Wu
AU - Jiadong Shi
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07285
UR - https://arxiv.org/abs/2611.07285
AB - Neutrino oscillations provide a natural setting for investigating the quantum character of flavor conversion and the distribution of quantum resources over macroscopic distances. Here, we study exact relations among purity-based first-order coherence, pairwise concurrence, and the maximal Clauser-Horne-Shimony-Holt (CHSH) value in coherent three-flavor neutrino oscillations. By expressing the evolving neutrino as a three-qubit single-excitation state, we derive the generally mixed two-qubit reductions and show that the squared first-order coherence of each flavor mode and its two associated squared concurrences sum to unity. Furthermore, a closed two-branch relation is obtained, showing that the maximal CHSH value of any reduced pair is determined by its average first-order coherence and concurrence. The branch structure follows from the correlation-tensor spectrum and yields exact conditions for CHSH violation. For the vacuum parameters and propagation ranges considered, electron preparation gives weak CHSH violations in electroncontaining pairs, while muon preparation produces a dominant utau pair with substantially stronger concurrence and Bell correlations. The comparison also identifies the thirdflavor contribution responsible for the different locations of concurrence and CHSH maxima. These results clarify the distribution of quantum correlations during flavor evolution and provide a basis for extensions to coherent matter propagation and wave-packet-induced mixed states.
ER -