Quantum estimation theory provides ultimate precision bounds on parameter estimation, independent of experimental setups. In this article, we apply this theoretical framework to neutrino oscillations, aiming to clarify some subtle issues and reveal the maximum achievable precision of oscillation parameters. First, taking the example of two-flavor oscillations, we clarify how the quantum Fisher information (QFI) depends on the choice of bases when the basis transformation itself involves the parameters in question. Then, for three-flavor oscillations, we compute the QFI matrix for electron and muon neutrino states in the flavor basis and derive analytical expressions and numerical results for both diagonal and off-diagonal elements. The implications of off-diagonal correlations for multiparameter estimation are discussed, and the quantum Cramér-Rao bounds on the precision of oscillation parameters for typical reactor and long-baseline accelerator neutrino experiments are obtained. Our results establish a theoretical benchmark for the ultimate precision achievable in future neutrino oscillation experiments.
Determination of the leptonic CP-violating phase
δCP, the atmospheric mixing angle
θ23, and the mass-squared difference
Δm312 constitutes a primary objective of current and next-generation long-baseline neutrino experiments. We employ Quantum Fisher Information (QFI) to quantify the maximum information that the neutrino quantum state contains about these oscillation parameters, treating the neutrino as an evolving pure quantum state. Computing the QFI as a function of the baseline-to-energy ratio
L/E for benchmark parameter sets from NuFit-6.0, we find distinct sensitivity hierarchies and
L/E-dependent structures. Specifically,
δCP and
θ23 exhibit bimodal QFI profiles with peaks around
L/E∼500 and
1500 km/GeV, reaching
FQ(δCP)∼0.15 and
FQ(θ23)∼15, respectively. In contrast,
FQ(Δm312) increases rapidly with
L/E over the range considered, reaching values of order
107. This hierarchy indicates that, within the considered single-parameter framework, the neutrino state carries substantially greater intrinsic quantum sensitivity to
Δm312 than to
θ23 or
δCP. We further compare the QFI with the classical Fisher information (CFI) obtained from flavor-transition probabilities, showing how much of the available information can be extracted through this specific measurement. For a fixed DUNE baseline, matter effects substantially enhance the QFI for
δCP in the few-GeV region, while producing only minor modifications for
θ23 and
Δm312. These results show that the information available for estimating the three oscillation parameters differs significantly, and that the flavor-probability measurement does not always extract all the information available in the quantum state.
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
θ13,
θ23, and
θ12, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for
δCP. In particular, only a small fraction of the available information on
δCP is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESS
νSB, a planned facility. Second, the QFI associated with
δCP 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
δCP 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.
Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor
ηp to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For
0<P<1 and
0<ηm<1, the QFIM in
(P,χ,ηm) is diagonal, with
Hχχmode=Cηm2 and
Hξmξmmode=Cηm2/(1−ηm2), where
ξm=−lnηm. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for
(θ23,δCP,ξ31,g) at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At
Γ0=10−23GeV, the fixed-coordinate ratio
Fδδflav/Hδδ is approximately
0.010,
0.013, and
0.105, respectively; all three points show strong
θ23--
ξ31 incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.
Neutrino oscillations are at the forefront of advances in Physics beyond the Standard Model. Increasing accuracy in measurements of the neutrino mixing matrix is an important challenge in current experiments. It depends on parameters that do not directly correspond to observables of the neutrino system. This type of estimation problem is handled by Quantum Estimation Theory (QET) via the Fisher Information (FI) and the Quantum Fisher Information (QFI). In this work, we analyze two-flavor neutrino oscillations within the framework of QET. We compute the QFI for the mixing angle
θ and show that mass measurements are the ones that achieve optimal precision. We also study the FI associated with flavor measurements and show that they are optimized at specific neutrino times-of-flight. Therefore, although the usual population measurement does not realize the precision limit set by the QFI, it can in principle be implemented with the best possible sensitivity to
θ. We study how these quantifiers relate to the single-particle, mode entanglement. We demonstrate that this form of entanglement does not enhance neither of them. In particular, this shows that in single-particle settings, entanglement is not directly connected with the optimal precision in metrological tasks.
The precise determination of the leptonic CP phase
δCP remains one of the central objectives of current and future long-baseline (LBL) neutrino oscillation experiments. Quantum estimation theory provides a natural framework to quantify the ultimate precision limits for estimating physical parameters encoded in quantum states. In this work, we employ the quantum Fisher information to investigate how much information about
δCP is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NO
νA. We first analyze the intrinsic quantum sensitivity of neutrino and antineutrino states and demonstrate how matter effects generate a neutrino mass-ordering dependent information structure. To compare the intrinsic information content of the quantum state with the information experimentally accessible through flavor measurements, we compute the event-level Fisher information from reconstructed event spectra using Poisson statistics. We find that both experiments extract only a small fraction of the total information available in the underlying quantum state. This extraction efficiency becomes particularly suppressed near maximally CP-violating regions, where the reconstructed event spectra exhibit reduced sensitivity to small variations in
δCP. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.