Coherent dynamics of flavor mode entangled neutrinos

As the lynchpin of all quantum correlations, quantum coherence is fundamental for distinguishing quantum systems from classical ones and is essential for realizing quantum advantages in areas such as computation, communication, and metrology. In this study, we investigate the relationship between quantum coherence and neutrino oscillations within the two and three flavor-mode qubit frameworks. Our analysis extends beyond the commonly used $l_1$-norm and relative entropy of coherence to include all relevant measures of coherence such as robustness of coherence, coherence concurrence, trace-norm distance measure of coherence, coherence of formation, Schatten-$p$-norm-based functionals, geometric coherence and logarithmic coherence rank, each offering unique insights into the quantum correlations in these systems. Notably, while the $l_1$-norm and relative entropy-based measures apply to general quantum states, the other measures are particularly relevant for entangled systems, highlighting the critical role of entanglement in neutrino oscillations. We present a detailed methodology for calculating coherence measures in both two-flavor and three-flavor mixing scenarios, contributing to a deeper understanding of how quantum coherence manifests and evolves in mode-entangled neutrino systems. Our findings emphasize the potential of these systems as robust candidates for quantum information tasks, facilitated by the weak interaction nature of neutrinos.