Quantum Fisher information (QFI) bounds state-encoded precision before measurement choice but does not establish identifiability, joint attainability, or detector sensitivity. We develop an operational framework for three-flavor oscillations that separates state, measurement, and reconstructed-event information. At fixed baseline, energy, source flavor, and matter profile, the propagated state is a pure qutrit, so its six-coordinate QFI has rank at most four. Resolved broadband components can restore rank because the aggregate kernel equals the intersection of their active kernels. We analyze joint attainability using quantum curvature, exact pure-state Holevo costs, and numerical primal-dual brackets, and propagate information through flavor projection, detector response, Poisson sampling, and nuisance profiling. An independent implementation of the public DUNE GLoBES configuration reproduces the reference spectra to relative error $3.87\times10^{-16}$ and the profiled likelihood curvature to $3.26\times10^{-6}$. Under the declared scaling and tolerance, its 264-bin event information has numerical rank six at all 176 documented physics points, whereas any four retained rule totals have rank at most four. The weakest record has effective rank five at the declared practical threshold. A conditional likelihood pilot also shows finite-grid overcoverage and dependence on the auxiliary-measurement ensemble. The framework identifies when local quantum or Fisher bounds do not support global experimental-sensitivity claims.
Quantum Fisher information (QFI) bounds state-encoded precision before measurement choice but does not establish identifiability, joint attainability, or detector sensitivity. We develop an operational framework for three-flavor oscillations that separates state, measurement, and reconstructed-event information. At fixed baseline, energy, source flavor, and matter profile, the propagated state is a pure qutrit, so its six-coordinate QFI has rank at most four. Resolved broadband components can restore rank because the aggregate kernel equals the intersection of their active kernels. We analyze joint attainability using quantum curvature, exact pure-state Holevo costs, and numerical primal-dual brackets, and propagate information through flavor projection, detector response, Poisson sampling, and nuisance profiling. An independent implementation of the public DUNE GLoBES configuration reproduces the reference spectra to relative error 3.87×10−16 and the profiled likelihood curvature to 3.26×10−6. Under the declared scaling and tolerance, its 264-bin event information has numerical rank six at all 176 documented physics points, whereas any four retained rule totals have rank at most four. The weakest record has effective rank five at the declared practical threshold. A conditional likelihood pilot also shows finite-grid overcoverage and dependence on the auxiliary-measurement ensemble. The framework identifies when local quantum or Fisher bounds do not support global experimental-sensitivity claims.
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.
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.
Leptonic CP Phase Determination from Fisher Information in NOνA and T2K
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 NOνA. 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.
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 1500km/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 ESSνSB, 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.
We investigate three-flavor neutrino oscillations within the framework of quantum estimation theory using the quantum Fisher information matrix (QFIM). We analyze all six independent elements of the QFIM for the parameters θ23, δCP, and Δm312, together with the corresponding quantum Cramér--Rao bounds and normalized parameter correlations. To connect the intrinsic quantum sensitivity of the neutrino state with experimentally accessible information, we further compare the QFI with the classical Fisher information (CFI) associated with flavor-probability measurements. We find that the difference between the quantum and classical information bounds is strongly dependent on the oscillation parameter and L/E, demonstrating that the efficiency with which the available quantum information is accessed depends on the measurement. We also investigate probability-degenerate solutions in the (θ23,δCP) parameter space. Although different parameter sets can produce identical νμ→νe appearance probabilities at specific L/E values, their corresponding quantum states can remain distinct, as demonstrated by the quantum fidelity. The QFIM differences further reveal distinct local quantum-information geometries for these probability-degenerate solutions, while the corresponding CFIM differences show a parameter and L/E dependent degree of distinguishability accessible through the flavor-probability measurement. Our results demonstrate that QFI and CFI provide complementary information for neutrino parameter estimation, with the QFIM serving as a measurement-independent quantum benchmark and the CFI characterizing the information accessible through a specified measurement.