Quantifying Information Hierarchy for Neutrino Oscillation Parameters at JUNO

Since neutrinos are quantum systems inherently, the precision with which oscillation parameters can be estimated ultimately depends on how much information about these parameters is encoded in the neutrino state and how efficiently that information can be extracted through measurement. In this work, we quantify how information encoded in reactor antineutrino states flows through the measurement process to the events observed at the detector, using quantum and classical Fisher information. We establish the information ladder for JUNO, revealing that the loss of precision across different information levels is strongly parameter dependent. We demonstrate that the JUNO configuration approaches the optimal statistical limit for the oscillation parameters of the solar sector, while information on ${\theta }_{13}$ and $\mathrm{\Delta }{m}_{31}^2$ is significantly degraded by the measurement strategy and detector effects. Despite this information loss, the remaining information is sufficient for JUNO to achieve sub-percent precision on $\mathrm{\Delta }{m}_{31}^2$ within six years.