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arXiv:2605.30404

Leptonic CP Phase Determination from Fisher Information in NO$ν$A and T2K

Neetu Raj Singh Chundawat, Luis A. Delgadillo, Yu-Feng Li

hep-phquant-phSubmitted May 28, 2026• Announced May 29, 2026• 0 citations
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Abstract

The precise determination of the leptonic CP phase $δ_{\rm CP}$ 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 $δ_{\rm CP}$ is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NO$ν$A. 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 $δ_{\rm CP}$. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.

Comments
29 pages, 10 figures

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Leptonic CP Phase Determination from Fisher Information in NOνννA and T2K
The precise determination of the leptonic CP phase δCPδ_{\rm CP}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 δCPδ_{\rm CP}δCP​ is intrinsically encoded in neutrino states and how efficiently it is extracted in present LBL experiments such as T2K and NOνννA. 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 δCPδ_{\rm CP}δCP​. Our analysis provides a complementary information-theoretic perspective on precise estimation of oscillation parameters in LBL neutrino experiments.
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Is the large uncertainty of δCPδ_{CP}δCP​ fundamentally encoded in the neutrino quantum state?
The precise measurement of the leptonic CP-violating phase δCPδ_{CP}δCP​ 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 δCPδ_{CP}δCP​ originates from intrinsic reasons, 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 δCPδ_{CP}δCP​ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESSνννSB proposal, substantially enhances δCPδ_{CP}δCP​ information compared to experiments centered on the first maximum.
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 θ13θ_{13}θ13​, θ23θ_{23}θ23​, and θ12θ_{12}θ12​, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for δCPδ_{CP}δCP​. In particular, only a small fraction of the available information on δCPδ_{CP}δCP​ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESSνννSB, a planned facility. Second, the QFI associated with δCPδ_{CP}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 δCPδ_{CP}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 present a quantum-information-theoretic study of three-flavor neutrino oscillations in long-baseline experiments by mapping flavor states to qubit-like representations and quantifying quantum correlations through total concurrence. The local minima of this entanglement measure identify energy regions where the flavor state is closest to separability, enabling cleaner extraction of oscillation parameters. We explain how these local minima offer opportunities for precision measurements and provide insight into the accurate determination of neutrino oscillation parameters. We then propose a strategy to improve parameter extraction by aligning the benchmark oscillation regions of NOνννA and T2K with the minimum entanglement achievable in each experiment. This shifts the concurrence minima toward higher-event-count energy regions, leading to tighter constraints and reducing the tension arising from their different energy regimes. For normal ordering, we obtain (0.581−0.0150+0.0136,195−32+38 ∘)(0.581^{+0.0136}_{-0.0150},195^{+38}_{-32}\,^\circ)(0.581−0.0150+0.0136​,195−32+38​∘) in the (sin⁡2θ23,δCP)(\sin^2θ_{23},δ_{\rm CP})(sin2θ23​,δCP​) plane and (0.580−0.0153+0.0140,2.515−0.0344+0.0344×10−3 eV2)(0.580^{+0.0140}_{-0.0153},2.515^{+0.0344}_{-0.0344}\times10^{-3}\,\mathrm{eV}^2)(0.580−0.0153+0.0140​,2.515−0.0344+0.0344​×10−3eV2) in the (sin⁡2θ23,Δm312)(\sin^2θ_{23},Δm^2_{31})(sin2θ23​,Δm312​) plane, yielding improved joint constraints. Using GLoBES simulations together with real data, we assess how local minima of quantum correlations influence leptonic CP-violation sensitivity, θ23θ_{23}θ23​ octant-degeneracy resolution, and mass-ordering determination. Our results show that minimizing entanglement can significantly affect these key sensitivities, highlighting quantum information measures as complementary probes of neutrino flavor oscillations and offering new insight into the role of quantum correlations in precision neutrino physics.
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.
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