Information-Theoretic Gaps in Solar and Reactor Neutrino Oscillation Measurements

TL;DR

This paper uses quantum estimation theory to compare the information content and precision limits of solar and reactor neutrino experiments in measuring key oscillation parameters, revealing fundamental differences in their sensitivities.

Contribution

It applies Quantum Fisher Information to analyze and contrast the fundamental information bounds in solar versus reactor neutrino measurements, clarifying their differing sensitivities.

Findings

Reactor neutrino flavor measurements are optimal and saturate the QFI bound.

Solar neutrino estimation of Δm²₁₂ is limited by classical, incoherent detection.

Solar experiments are more sensitive to θ₁₂ than to Δm²₁₂.

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, $\Delta m^2_{21}$ and $\theta_{12}$, 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 $\Delta m_{21}^2$ purely population-based and effectively classical, while the QFI for $\theta_{12}$ is dominated by basis rotation at high energies and is nearly saturated by flavor measurements. Consequently, solar neutrino experiments are intrinsically more sensitive to $\theta_{12}$ than to $\Delta m_{21}^2$. This analysis highlights a fundamental distinction between the two estimation problems and accounts for their differing achievable precisions.