Quantum Estimation Theory Limits in Neutrino Oscillation Experiments

Abstract

Measurements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing parameters have entered a precision era, enabling increasingly stringent tests of neutrino oscillations. Within the framework of quantum estimation theory, we investigate whether flavor measurements, the only observables currently accessible experimentally, are optimal for extracting the oscillation parameters. We compute the Quantum Fisher Information (QFI) and the classical Fisher Information (FI) associated with ideal flavor projections for all oscillation parameters, considering accelerator muon (anti)neutrino and reactor electron antineutrino beams propagating in vacuum. Two main results emerge. First, flavor measurements saturate the QFI at the first oscillation maximum for $θ_{13}$, $θ_{23}$, and $θ_{12}$, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for $δ_{CP}$. In particular, only a small fraction of the available information on $δ_{CP}$ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS$ν$SB, a planned facility. Second, the QFI associated with $δ_{CP}$ is approximately one order of magnitude smaller than that of the mixing angles, indicating that the neutrino state intrinsically encodes less information about CP violation. Nevertheless, this quantum bound lies well below current experimental uncertainties, implying that the present precision on $δ_{CP}$ is not fundamentally limited. Our results provide a quantitative framework to disentangle fundamental from practical limitations and establish a benchmark for optimizing future neutrino facilities.

Figures (11)

• Figure 1: Neutrino oscillations as a quantum metrology protocol: a neutrino with a specific flavor $\alpha$ is prepared at time $t=0$. After evolving for a time $t$ the neutrino quantum state can be written as a superposition of flavor eigenstates, with coefficients that depends on the different parameters ${\bf \lambda}$ that characterize the neutrino oscillations. A final measurement (typically corresponding to a flavor detection) is performed on the output state.
• Figure 2: QFI $H_{\nu,\overline{\nu}}(\delta_{CP})$ obtained with a $\nu_\mu / \overline{\nu}_\mu$ beam (green solid line) as a function of the baseline/energy ratio $L/E$. The dashed black and blue curves show the appearance probabilities $P(\nu_{\mu }\to \nu_e)$ and $P(\bar{\nu}_{\mu} \to \bar{\nu}_e)$, respectively. For T2K/T2HK we considered $L=295$ km and a peak energy of 0.6 GeV, while for ESS$\nu$SB $L=360$ km and a peak energy of 0.25 GeV.
• Figure 3: QFI $H_{\nu,\overline{\nu}}(\delta_{CP})$ obtained with a $\nu_\mu / \overline{\nu}_\mu$ beam (green solid line) and QFI $H_{\overline{\nu}_e}(\delta_{CP})$ obtained with a $\nu_e$ beam (purple solid line) as a function of the ratio $L/E$ between baseline and beam energy. For T2K/T2HK we considered $L=295$ km and a peak energy of 0.6 GeV, while for ESS$\nu$SB $L=360$ km and a peak energy of 0.25 GeV.
• Figure 4: QFI for $\theta_{23}$ (bordeaux) and $\theta_{13}$ (orange) for a muon (anti)neutrino beam. For T2K/T2HK we considered $L=295$ km and a peak energy of 0.6 GeV, while for ESS$\nu$SB $L=360$ km and a peak energy of 0.25 GeV.
• Figure 5: QFI $H_{\bar{\nu}_e}(\theta_{12})$ (a) and $H_{\bar{\nu}_e}(\theta_{13})$ (b) for an electron antineutrino beam. In black the oscillation probability $P(|\overline{\nu}_e\rangle \to |\overline{\nu}_\mu\rangle)$ (multiplied by 5 in (a) and by 15 in (b)). For KamLand $L=180$km and the peak energy lies between 3-4 MeV and we choose $E=3.6$ MeV. For Daya Bay $L=1.64$ km and we considered a peak energy of 3 MeV.