The precise measurement of the leptonic CP-violating phase ${\delta }_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in ${\delta }_{CP}$ originates from intrinsic properties—either of the neutrino quantum state or of flavor measurements—or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to ${\delta }_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that, while targeting the second oscillation maximum, as in the $\mathrm{ESS}\nu \mathrm{SB}$ proposal, typically enhances ${\delta }_{CP}$ information, this feature in fact strongly depends on the actual values of ${\delta }_{CP}$.

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• Particle mixing & oscillations
• Phenomenology
• Quantum metrology
• Quantum parameter estimation