Information-Theoretic Gaps in Solar and Reactor Neutrino Oscillation Measurements

TL;DR

This work applies quantum estimation theory to neutrino oscillations, contrasting the information content available in reactor (coherent vacuum) and solar (incoherent MSW) environments for the solar parameters $Δm^2_{21}$ and $θ_{12}$. It shows that reactor neutrinos possess phase information that can saturate the quantum Fisher bound for both parameters at certain energies, while solar neutrinos lack phase information, making $θ_{12}$ information largely population- and rotation-driven and $Δm^2_{21}$ information comparatively limited. By decomposing the QFI into population and rotation contributions and deriving explicit FI expressions for both setups, the paper explains why reactor experiments like KamLAND and JUNO achieve high precision for both parameters, whereas solar experiments preferentially constrain $θ_{12}$. The results provide a quantitative, theory-grounded explanation for experimental sensitivities and offer a framework to optimize parameter estimation across current and future neutrino experiments, including extensions to the full three-flavor sector and multiparameter estimation.

Abstract

Quantum estimation theory provides a fundamental framework for analyzing how precisely physical parameters can be estimated from measurements. Neutrino oscillations are characterized by a set of parameters inferred from experiments conducted in different production and detection environments. The two solar oscillation parameters, $Δm^2_{21}$ and $θ_{12}$, can be estimated using both solar neutrino experiments and reactor neutrino experiments. In reactor experiments, neutrinos are detected after coherent vacuum evolution, while solar neutrinos arrive at the detector as incoherent mixtures. In this work, we use Quantum Fisher Information (QFI) to quantify and compare the information content accessible in these two experimental setups. We find that for reactor neutrinos, flavor measurements saturate the QFI bound for both parameters over specific energy ranges, demonstrating their optimality and explaining the high precision achieved by these experiments. In contrast, for solar neutrinos the phase-based contribution to the QFI, originating from the quantum coherence, is absent, rendering the estimation of $Δm_{21}^2$ purely population-based and effectively classical, while the QFI for $θ_{12}$ is dominated by basis rotation at high energies and is nearly saturated by flavor measurements. Consequently, solar neutrino experiments are intrinsically more sensitive to $θ_{12}$ than to $Δm_{21}^2$. This analysis highlights a fundamental distinction between the two estimation problems and accounts for their differing achievable precisions.

Figures (3)

• Figure 1: The extracted fraction $\eta^{\nu}$ for reactor neutrinos as a function of the neutrino energy $E$ for KamLAND and JUNO baselines. The red solid (dashed) curve corresponds to $\eta^{\nu}$ for $\theta_{12}$, the blue solid (dashed) curve represents $\eta^{\nu}$ for $\Delta m_{21}^2$ for JUNO (KamLAND), and the black dotted line denotes the quantum limit set by the QFI.
• Figure 2: The left panel shows the Fisher information for $\theta_{12}$, while the right panel corresponds to $\Delta m_{21}^2$ as a function of neutrino energy $E$ for solar neutrinos. In the left panel, the blue curve denotes the QFI, the orange curve represents the population contribution, and the green curve shows the Fisher information associated with the flavor POVM. In the right panel, the blue and green curves correspond to the QFI and the flavor POVM Fisher information for $\Delta m_{21}^2$, respectively. The electron-neutrino survival probability $P_{ee}^\odot$ is indicated by the black dot-dashed curve, and the MSW resonance point is marked by the black dotted line.
• Figure 3: Extracted fraction $\eta^{\odot}$ as a function of the neutrino energy $E$ for solar neutrinos. The magenta and cyan curves correspond to $\eta^{\odot}$ for $\theta_{12}$ and $\Delta m_{21}^2$, respectively.